International Conference on Statistical Distributions and Applications
ICOSDA 2016

Oct. 14-16, 2016, Crowne Plaza,  Niagara Falls, Canada

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Important Deadlines

 

Titles and abstracts are updated shown below on September 6th

Please take a look at your title and abstract. Please e-mail carl.lee@cmich.edu , if there is any revision needed.

 

Titles and abstracts for Keynote and Plenary speakers are on the ‘Keynotes & Plenary Speakers’ Page.

 

Topic-Invited Sessions: Topics and Organizers

 

Room Abbreviation: NI – Niagara Room, BR - Brock Room, EL – Elisabeth Room, CAN/B – Canadian Room/B

 

Session

Topic

Organizer

Date

Time

Room

TI 1

Applications of Statistical Distributions in Business, Management and Economics

Sarabia, Jose Maria

Oct 15

9:15 am -10:35 am

NI

TI 2

Some Recent Issues and Methods in Statistics and Biostatistics

Yi, Grace 

Oct 15

9:15 am -10:35 am

BR

TI 3

Relative Belief Inferences

Evans, Michael

Oct 15

9:15 am -10:35 am

EL

TI 4

Recent developments in designs and analysis of statistical experiments

Xu, Xiaojian

Oct 15

9:15 am -10:35 am

CAN/B

TI 5

Generalized distributions and its application

Alzaatreh, Ayman 

Oct 15

3:00 pm -4:20pm

NI

TI 6

Don’t Count on Poisson! Introducing the Conway-Maxwell-Poisson distribution for statistical methodology regarding count data

Sellers, Kimberly 

Oct 15

3:00 pm -4:20pm

BR

TI 7

Extreme Value Distributions and Models

Huang,  Mei-Ling

Oct 15

3:00 pm -4:20pm

EL

TI 8

Moment-Based Methodologies for Approximating and Estimating Density Functions

Provost, Serge B. 

Oct 15

3:00 pm -4:20pm

CAN/B

TI 9

Dependence modelling with applications in insurance and finance

Furman, Edward

Oct 16

9:15 am -10:35 am

NI

TI 10

Multivariate distributions

Richter, Wolf-Dieter 

Oct 16

9:15 am -10:35 am

BR

TI 11

Bayesian analysis for highly structured processes

Ferreira, Marco A. R. 

Oct 16

9:15 am -10:35 am

EL

TI 12

Recent development on Complex Data Analysis

Gao, Xiaoli

Oct 16

9:15 am -10:35 am

CAN/B

TI 13

Copula Modeling of Discrete Dependent Data

De Oliveira, Victor 

Oct 16

10:50 am -12:10 pm

NI

TI 14

Statistics and Modelling

Stehlik, Milan 

Oct 16

10:50 am -12:10 pm

CAN/B

TI 15

Copula Theory and Applications to Insurance and Finance

Cooray, Kahadawala 

Oct 16

3:00 pm -4:20pm

NI

TI 16

Bayesian approaches on models and distributions estimation

Cheng, Chin-I 

Oct 16

3:00 pm -4:20pm

BR

TI 17

Compounding and Copulas:  Generalized and Extended Distributions

Oluyede, Broderick O. 

Oct 16

3:00 pm -4:20pm

EL

TI 18

Modeling complex data

Amezziane, Mohamed 

Oct 16

3:00 pm -4:20pm

CAN/B

TI 19

Mixtures of Non-Gaussian Distributions with Applications in Clustering

McNicholas, Paul 

Oct 16

4:30 pm -5:50 pm

NI

TI 20

Likelihood-based Inference: Methods and Applications

Coelho, Carlos A. 

Oct 16

4:30 pm -5:50 pm

BR

TI 21

Statistical Methods for Analysis of Industrial and Medical Data

Ng, Hon Keung Tony 

Oct 16

4:30 pm -5:50 pm

EL

TI 22

Construction of new statistical distributions and statistical data modeling

Akinsete, Alfred

Oct 16

4:30 pm -5:50 pm

CAN/B

 

 

Abstracts – Topic-Invited Speakers (Alphabetically Ordered)

 

Session Name: TI m_k (m_k =  kth speaker in the mth session)

TI 22_3

Al-Aqtash, Raid

Title

Gumbel-Burr XII {logistic}  distribution

In this project, a member of the Gumbel-X family of distributions is defined. Many properties will be presented including shapes, moments, skewness, kurtosis, parameter estimation. The distribution will be used to fit real life data and compare the performance with other used probability distributions.

TI 3_4

Al-Labadi, Luai

Title

Prior-based model checking

Model checking procedures are considered based on the use of the Dirichlet process and relative belief. This combination is seen to lead to some unique advantages for this problem.

TI 5_4

Alzaatreh, Ayman

Title

Parameter estimation for the log-logistic distribution based on order statistics

In this talk, the moments and product moments of the order statistics in a sample of size n drawn from the log-logistics distribution are discussed. We provide more compact forms for the mean, variance and covariance of order statistics. Parameter estimation for the log-logistic distribution based on order statistics is studied. In particular, best linear unbiased estimators (BLUEs) for the location and scale parameters for the log-logistic distribution with known shape parameter are studied. Hill estimator is proposed for estimating the shape parameter.

TI 10_2

Arslan, Olcay

Title

A unified approach to some multivariate skew distributions

The main objective of the present work is to introduce a unified class of skew and heavy-tailed distributions. We construct the new class by defining the variance–mean mixture of a skew normal distributed random variable  with a positive scalar-valued random variable independent of the skew normal  distributed random variable. The new class can be regarded as an extension of the following classes: the normal variance mixture distributions, the variance mixture of the skew normal distribution and the normal variance–mean mixture distributions. An explicit expression for the density function of the new class is given and some of its distributional properties are examined. We give a simulation algorithm to generate random variates from the new class and propose an EM algorithm for maximum likelihood estimation of its parameters.

TI 17_1

Baharith, Lamya A.

Title

Bivariate Truncated Type I Generalized Logistic Distribution

Truncated type I generalized logistic distribution has been used in variety of applications.  In this article, new bivariate truncated type I generalized logistic distribution based on different types of copula functions is introduced. A study of some properties is illustrated. Different methods of estimation are used to estimate the parameters of the proposed distribution. Monte Carlo simulation is carried out to examine the performance of the estimators. Finally, real data set is analyzed to illustrate the satisfactory performance of the proposed distribution.

TI 7_1

Brill , Percy and Huang, Mei Ling

Title

A Renewal Process for Extremes

We derive the finite time-t probability density function (pdf) of the excess, age, and total life of a renewal process where inter-arrival times have a heavy tailed distribution, namely, a no-mean Pareto distribution with shape parameter Alpha in (0,1]. We compare the time-t pdf’s with the corresponding limiting pdf’s of a renewal process with inter-arrival times distributed as a finite-mean, truncated Pareto distribution having the same shape parameter Alpha. We give an example with fixed value t, and right truncation point K, such that the corresponding limiting pdf’s closely approximate the finite time-t pdf’s on a subset of support.

TI 16_2

Chatterjee, Arpita

Title

A note on Dirichlet Process based semiparametric Bayesian models

Semiparamatric Bayesian models have become increasingly popular over the past few decades. As compared to their parametric counterparts, the semiparametric models allow for a greater flexibility in capturing the parameter uncertainty. Dirichlet process mixed models form a particular class of Bayesian semiparametric models by assuming a random mixing distribution, taken to be a realization from a Dirichlet process, for the mixture. In this research, we show that while hierarchical DP models may provide flexibility in model fit, they may not perform uniformly better in other aspects as compared to the parametric models.

TI 16_4

Cheng, Chin-I

Title

Bayesian Estimators of the Odd Weibull distribution with censored data

The Odd Weibull distribution is a three-parameter generalization of the Weibull distribution. The Bayesian methods with Jeffreys priors for estimating parameters of the Odd Weibull with censored data is considered. The Adaptive Rejection Sampling (ARS) and Adaptive Rejection Metropolis Sampling (ARMS) are adapted to generate random samples from full conditionals for inferences on parameters. The estimates based on Bayesian and maximum likelihood on censored data are compared. In order to clarify and advance the validity of Bayesian and likelihood estimators of the Odd Weibull distribution, one simulated data set and two examples about failure time are analyzed.

TI 6_3

Choo-Wosoba, Hyoyoung

Title

Marginal Regression Models for Clustered Count Data Based on Zero-Inflated Conway-Maxwell-Poisson Distribution with Applications

We propose a marginal regression model with a Conway-Maxwell-Poisson (CMP) distribution for clustered count data exhibiting excessive zeros and a wide range of dispersion patterns. Two estimation methods (MPL and MES) are introduced. Finite sample behaviors of the estimators and the resulting confidence intervals are studied using an extensive simulation study. We apply our methodologies to the data from the Iowa Fluoride Study and identify significant protective and risk factors from dietary and non-dietary covariates. We also provide an application of an under-dispersion case with a maize Hybrids experiment data.

TI 14_4

Christara, Christina C.

Title

PDE option pricing with variable correlations

Correlation between financial quantities plays an important role in pricing financial derivatives. Existing popular models assume that correlation either is constant, or exhibits some deterministic behaviour. However, market observations suggest that correlation is a more complicated process. We consider correlation structures that are guided by regime switching or by a stochastic process. We derive the related Partial Differential Equation (PDE) problems for pricing several types of financial derivatives, and solve them by accurate and efficient numerical methods. We also study the effect of model parameters to the prices. We present the PDE, the numerical solution, and comparison of the PDE results to Monte-Carlo simulations. We also discuss the relevant numerical challenges. This is joint work with Chun Ho (Nat) Leung.

TI 20_4

Coelho, Carlos A.

Title

Likelihood ratio test for the equality of mean vectors when the joint covariance matrix is block-circulant or block compound symmetric

The test developed and presented may be seen not only as a generalization of the common test of equality of mean vectors, under the assumption of independence of the corresponding random vectors or of independence of the samples, as well as a generalization of the tests for equality of means under the assumptions of a circulant or compound symmetric covariance matrix. Since the exact p.d.f. and c.d.f. of this likelihood ratio statistic do not have tractable expressions, near-exact distributions are developed, which enable the easy obtainment of sharp quantiles and p-values, and as such the practical implementation of these tests.

TI 15_4

Cooray, Kahadawala

Title

Strictly Archimedean Copula with Complete Association for Multivariate Dependence Based on the Clayton Family

The Clayton copula is one of the most discussed Archimedean copulas for dependency measurement. However, the major drawback is that when it accounts for negative dependence, the copula becomes nonstrict and its support depends on the parameter. To address this issue, this talk introduces a new two-parameter family of strict Archimedean copula to measure exchangeable multivariate dependence. Closed-form formulas for the complete monotonicity and the d−monotonicity parameter region of the generator, copula distribution function, and the Kendall’s distribution function are derived. Simulation studies are conducted to assess the performance of the ml estimators of the d−variate copula under known margins.

TI 9_1

Cossette,Hélène/Itre Mtalai/Etienne Marceau/Déry Veilleux

Title

Archimedean copulas: Aggregation and capital allocation

Risk aggregation evaluates the distribution of the sum of n random variables which represent individual risks. Researchers in insurance and finance have investigated the aggregation of dependent risks to determine an adequate level of capital to offset the global risk S=X+…+ Xn of a portfolio of n risks with known joint distribution. Risk measures, such as the VaR and TVaR, can be used to calculate the minimum capital requirement associated to S and the amount of capital allocated for each risk within the portfolio. We consider a portfolio of dependent risks represented by a vector of positive random variables whose joint distribution function is defined by a copula C and its margins F1, ...,Fn. We assume that the copula C is either an Archimedean copula or a nested Archimedean copula. Our objective is to introduce a deterministic method of computation of the distribution of S which relies on the fact that an Archimedean copula can be represented as a common mixture with a positive mixing variable. The exchangeability property of Archimedean copulas restricts their application. We hence extend some results to nested Archimedean copulas and propose a different approach permitting to get around certain constraints of these copulas.

TI 19_1

Dang, Sanjeena

Title

Mixtures of Dirichlet-Multinomial Regression Models for Microbiome Data

The human gut microbiome is a source of great genetic and metabolic diversity. Microbiome samples which share similar biota compositions are known as enterotypes. Exploring the relationship between biological/environmental covariates and the taxonomic composition of the gut microbial community can shed light on the enterotype structure. Dirichlet-multinomial models have been previously suggested to investigate this relationship, however these models did not account for any latent group structure. Here, a finite mixture of Dirichlet-multinomial regression models is proposed and illustrated. These models allow for accounting for the enterotype structure and allow for a probabilistic investigation of the relationship between bacterial abundance and biological/environmental covariates within each inferred enterotype. Furthermore, a generalization of these models is also proposed that can incorporate the concomitant effect of the covariates on the resulting mixing proportions.

TI 19_3

Dang, Utkarsh

Title

Parsimonious skew power-exponential mixture models

A family of parsimonious mixtures of multivariate power exponential distributions is presented. The multivariate power exponential distribution is a flexible elliptical alternative to the Gaussian and Student t-distributions, allowing for dealing with both varying tail-weight (light or heavy) and peakedness of data. For particular values of the shape parameter, special and limiting cases of this distribution include the double-exponential, Gaussian, and the uniform distributions. Furthermore, an extension of these models is presented that can also model asymmetric data. Computational and inference challenges will be discussed. Lastly, the utility of the proposed models is illustrated using both toy and benchmark data.

TI 13_4

De Oliveira, Victor

Title

On the Correlation Structure of Gaussian Copula Models for Geostatistical Count Data

We describe a class of random field models for geostatistical count data based on Gaussian copulas. Unlike hierarchical Poisson models often used to describe this type of data, Gaussian copula models allow a more direct modelling of the marginal distributions and association structure of the count data. We study in detail the correlation structure of these random fields when the family of marginal distributions is either negative binomial or zero-inflated Poisson; these represent two types of overdispersion often encountered in geostatistical count data. We also contrast the correlation structure of one of these Gaussian copula models with that of a hierarchical Poisson model having the same family of marginal distributions, and show that the former is more flexible than the latter in terms of range of feasible correlation, sensitivity to the mean function and modelling of isotropy. An exploratory analysis of a dataset of Japanese beetle larvae counts illustrate some of the findings. All of these investigations show that Gaussian copula models are useful alternatives to hierarchical Poisson models, specially for geostatistical count data that display substantial correlation and small overdispersion.

TI 3_1

Evans, Michael

Title

Measuring Statistical Evidence Using Relative Belief

A fundamental concern of any theory of statistical inference is how one should measure statistical evidence. Certainly the words `statistical evidence', or

perhaps just 'evidence', are much used in statistical contexts. Still it is fair to say that the precise characterization of this concept is somewhat

elusive. Our goal here is to provide a definition of how to measure statistical evidence for any particular statistical problem. Since evidence is what causes

beliefs to change, we measure evidence by the change in belief from a priori to a posteriori. As such our definition involves prior beliefs and this raises issues of subjectivity versus objectivity in statistical analyses. We deal with this through a principle requiring the falsifiability of any ingredients to a statistical analysis. This leads to a discussion of checking for prior-data conflict and measuring the a priori bias in a prior.

TI 12_3

Fang, Yixin

Title

Variable selection for partially linear models via learning gradients

The performance of the proposed estimator is demonstrated in both simulation studies and real examples. Partially linear models, a compromise between parametric regression and non-parametric regression models, are very useful for analyzing high-dimensional data. Variable selection plays an important role in the use of partially linear models, which are of both linear and non-linear components. Variable selection for the linear component has been well studied. However, variable selection for the non-linear component usually relies on some assumption imposed on the structure of the non-linear component. For example, variable selection methods have been developed for additive partially linear models and generalized additive partially linear models. In this manuscript, we propose a new variable selection method based on learning gradients for partially linear models without any assumption on the structure of the non-linear component. The proposed method utilizes the reproducing-kernel-Hilbert-space tool to learn the gradients and the group-lasso penalty to select variables. In addition, a block-coordinate descent algorithm is described and some theoretical properties are derived. The performance of the proposed method is evaluated via simulation studies and a real data application.

TI 14_2

Filus, Jerzy 

Title

Two Kinds of Stochastic Dependencies Bi-variate Distributions; Part 2

A new class of bivariate probability densities as stochastic models for some biomedical as well as for reliability phenomena is constructed. The models are fusions of the already known bivariate “pseudodistributions” (pseudoexponential and pseudoWeibulian, in particular) with a rather new class of bivariate survival functions that, basically, look like a generalization of the first bivariate Gumbel’s survival function. This generalization is obtained by use of ‘additive hazard models’ (see, Aalen, 1989) which are some modifications of the famous model by Cox (1972). The class of the “Gumbel-like” models, we will present, is quite general so that it, possibly, contains “most of” bivariate survival functions met in practical applications. In biomedical (or reliability) situations, we consider, a member of this class is supposed to model some particular stochastic dependence between biomedical quantities according to a bio-physical phenomena. In addition, stochastic description of some other, more complex type of phenomena, one obtains by applying to the previous bivariate distribution a pseudo-linear transformation of the random vector possessing the previously mentioned property of being the “Gumbel-like” distributed. The pseudo-linear transformation once applied to independent random variables produces the pseudodistributions. In the case it is applied to the random variables having the joint Gumble-like distributions one obtains the fusion of two different stochastic models. Some analysis of the “combined” bivariate distributions will be presented.

TI 14_1

Filus, Lidia

Title

Two Kinds of Stochastic Dependencies Bi-variate Distributions; Part 1

A new class of bivariate probability densities as stochastic models for some biomedical as well as for reliability phenomena is constructed. The models are fusions of the already known bivariate “pseudodistributions” (pseudoexponential and pseudoWeibulian, in particular) with a rather new class of bivariate survival functions that, basically, look like a generalization of the first bivariate Gumbel’s survival function. This generalization is obtained by use of ‘additive hazard models’ (see, Aalen, 1989) which are some modifications of the famous model by Cox (1972). The class of the “Gumbel-like” models, we will present, is quite general so that it, possibly, contains “most of” bivariate survival functions met in practical applications. In biomedical (or reliability) situations, we consider, a member of this class is supposed to model some particular stochastic dependence between biomedical quantities according to a bio-physical phenomena. In addition, stochastic description of some other, more complex type of phenomena, one obtains by applying to the previous bivariate distribution a pseudo-linear transformation of the random vector possessing the previously mentioned property of being the “Gumbel-like” distributed. The pseudo-linear transformation once applied to independent random variables produces the pseudodistributions. In the case it is applied to the random variables having the joint Gumble-like distributions one obtains the fusion of two different stochastic models. Some analysis of the “combined” bivariate distributions will be presented.

TI 19_2

Gallaugher, Michael

Title

Clustering Clickstream Data Using a Mixture of Continuous Time Markov Models

In today's society, the internet is quickly becoming a major source of data. One interesting type of data that can be utilized from the internet is clickstream data, which monitors a user's web browsing patterns. Clustering is the process of finding underlying group structures in a dataset, and although there has been ample work done in the clustering paradigm for clickstream data, the methods often neglect the amount of time spent on each website.  By failing to include a time component in the model, we are robbing ourselves of potentially valuable information. We propose a mixture of continuous time first order Markov models for the clustering of clickstreams which would incorporate the time aspect. Both simulated data, and real datasets will be considered for the evaluation of the proposed methodology.

TI 5_3

Ghosh, Indranil

Title

Some alternative bivariate Kumaraswamy models

In this paper we discuss various strategies for constructing bivariate Kumaraswamy distributions. As alternatives to the Nadarajah, Cordeiro and Ortega (2011) bivariate model, four different models are introduced utilizing a conditional specification approach, a conditional survival function approach, an Arnold-Ng bivariate beta distribution construction approach, and a copula based construction approach. Distributional properties for such bivariate distributions are investigated. Parameter estimation strategies for the models are discussed, as are the consequences of fitting two of the models to a particular data set involving hemoglobin content in blood samples before and after treatment.

TI 18_4

Giurcanu, Mihai

Title

Thresholding Least Squares Inference in High Dimensional Regression Models 

We propose a thresholding least-squares method of inference for high-dimensional regression models when the number of parameters, p, tends to infinity with the sample size, n. Extending the asymptotic behavior of the F-test in high dimensions, we establish the oracle property of the thresholding least-squares estimator when p = o(n). We propose two automatic selection procedures for the thresholding parameter using Scheffe and Bonferroni methods. We show that, under additional regularity conditions, the results continue to hold even if p = exp(o(n)). Lastly, we show that, if properly centered, the residual-bootstrap estimator of the distribution of thresholding least-squares estimator is consistent, while a naive bootstrap estimator is inconsistent. In an intensive simulation study, we assess the finite sample properties of the proposed methods for various sample sizes and model parameters. The analysis of a real world data set illustrates an application of the methods in practice.

TI 1_2

Gomez-Deniz, Emilio

Title

Computing Credibility Bonus-Malus Premiums Using a Bivariate Discrete Distribution

A simple modification for computing the automobile insurance bonus-malus premiums is proposed here. Traditionally, in automobile insurance the premium assigned to each policyholder is based only on the number of claims made. Therefore, a policyholder who has had an accident producing a relatively small amount of loss is penalised to the same extent as one who has had a more costly accident and this seems to be unfair. We propose a statistical model which distinguishes between two different types of claims, incorporating a bivariate distribution based on the assumption of dependence. We also describe a bivariate prior distribution conjugated with respect to the likelihood. This approach produces credibility bonus-malus premiums that satisfy appropriate transition rules. A practical example of its application is presented and the results obtained are compared with those derived from the traditional model in which only the number of claims is taken into account.

TI 5_2

Hamedani, Gholamhossein

Title

Characterizations of Probability Distribution Via the Concept of Sub-Independence

Limit theorems as well as other well-known results in probability and statistics are often based on the distribution of the sums of independent (and often identically distributed) random variables rather than the joint distribution of the summands. Therefore, the full force of independence of the summands will not be required. In other words, it is the convolution of the marginal distributions which is needed, rather than the joint distribution of the summands. The concept of sub-independence, which is much weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. In this talk, certain characterizations of probability distributions based on the concept of sub-independence will be presented.

TI 16_1

He, Jianghua

Title

Bayesian Reliability Assessment of Facility-Level Patient Outcome Measures

Patient health outcome measures at facility-level are often used as quality indicators of patient care. Within-facility variations of such measures often differ among facilities. The intraclass correlation coefficient based on equal within-subject variation may not be directly applied. Signal-to-noise approach can be used to assess the facility-specific reliability of a measure with different within-subject variation among facilities. In this study, we propose a new approach of assessing the reliability of patient outcome measures at facility-level in differentiating one facility from others by allowing for facility-specific variation. The Bayesian framework is utilized to handle measures of events rates with non-negligible zeros.

TI 2_2

He, Wenqing

Title

Improving Performance of Support Vector Machine Classifiers with Data Adaptive Kernel

Support Vector Machine (SVM) is popularly used in the classification/prediction of discrete outcomes, especially in high dimensional data analysis such as gene expression data analysis and image analysis. In this talk, a new enhance SVM method will be presented. The initial kernel function for the SVM is rescaled in an adaptive way so that the separation between two classes can be effectively enlarged, based on the prior knowledge obtained from the conventional SVM. The modified classifier takes into consideration the distribution of the support vectors in the feature space, and the correlation will be dealt with by selecting only limited numbers of parameters properly. Improvement of prediction accuracy from this data dependent SVM is shown with numerical studies.

TI 12_1

Hirose, Kei

Title

Robust estimation for sparse Gaussian graphical model

In Gaussian graphical modeling, we often use a penalized maximum likelihood approach with the L1 penalty for learning a high-dimensional graph. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the \gamma-divergence. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. This method has a redescending property, which is known as a desirable property in robust statistics. Extensive simulation studies showed that our procedure performed much better than the existing methods.

TI 7_3

Hlynka, Myron

Title

Comments on the Gumbel Distribution

The talk will discuss the Gumbel distribution and its relationship to integer partitions.

TI 11_4

Hoegh, Andrew

Title

Multiscale Spatiotemporal Modeling for Predicting Civil Unrest

Civil unrest is a complicated, multifaceted social phenomenon that is difficult to forecast. Relevant data for predicting future protests consist of a massive set of heterogeneous data sources, primarily from social media. A modular approach to extract pertinent information from disparate data sources is implemented to develop a multiscale spatiotemporal framework to fuse predictions from algorithms mining social media. The novel multiscale spatiotemporal framework is scalable to handle massive spatiotemporal datasets and can incorporate hierarchical covariates. An efficient sequential Monte Carlo procedure coupled with the multiscale framework enables rapid computation of a richly specified Bayesian hierarchical model for spatiotemporal data.

TI 13_1

Hughes, John

Title

Hierarchical Copula Regression Models for Areal Data

Regression analysis for spatially aggregated data is common in a number of fields, including public health, ecology, and econometrics. Often, the goal of such an analysis is to quantify the relationship between an outcome of interest and one or more covariates. The mixed model with proper conditional autoregressive (CAR) spatial random effects is commonly used to model such data but suffers serious drawbacks. First, an analyst must interpret covariate effects conditionally although marginal effects may be of interest. Second, the dependence parameter of the proper CAR model has an intuitive conditional interpretation, but the parameter's marginal interpretation is complicated and counterintuitive; specifically, spatial units with a similar number of neighbors have different marginal correlations. To overcome these two drawbacks, we propose a copula-based hierarchical model with covariance selection. Our approach allows for unbiased estimation of marginal parameters and thus an
intuitive marginal interpretation. The covariance-selection copula's single dependence parameter is the first-order correlation. This provides a dependence structure having intuitive conditional and marginal interpretations. We develop a computational framework that permits efficient frequentist inference for our model, even for large datasets. We evaluate the small- and large-sample performance of our method under simulated conditions, and apply our procedure to a widely studied Slovenia stomach cancer dataset.

TI 14_3

IshimuraNaoyuki

Title

Evolution of copulas and its applications

Copula is known to provide a flexible method for the understanding of dependence structure among random events. However, a copula

function does not usually involve a time variable. We have developed, on the other hand, the concept of evolution of copulas, which claim that

copula itself evolves according to the time variable. In this presentation, we review our recent study on this evolution of copulas and consider

its applications, which include in particular the analysis of exchange rate modeling.

TI 3_2

Jang, Gun Ho  and Stein, Lincoln

Title

Relative Belief based Signal Segmentation

Cancers display a considerable degree of genomic copy number alteration (CNA), manifested as chromosomal and segmental amplifications and deletions. Many CNA detection algorithms assume the events follow a locally constant signal model, but low tumor fractions and/or subclonal heterogeneity create weak signals that are difficult to interpret accurately. We propose a segmentation method using a relative belief inference on a locally constant model. The performance of the proposed method is presented and compared with several segmentation algorithms including circular

binary segmentation, allele-specific piecewise constant fitting and SCAN algorithms.

TI 21_2

Jayalath, Kalanka

Title

A Graphical Test for Testing Random Effects in Common Statistical Designs

Analysis of means (ANOM) is a powerful graphical testing procedure for comparing means and variances in fixed effect models. The graphical interpretation of ANOM is a great advantage over the classical ANOVA approach. However, the ANOM only deals with the fixed factor effects. In this talk, we discuss the ability to extend the ANOM approach to testing random effects. We also discuss the use of the new ANOM approach in many different statistical designs including both random and mixed effects models with illustrative examples. The power performance of the proposed procedure is compared to the ANOVA approach via a simulation study.

TI 9_4

Jevtić, Petar/Hurd, Thomas R.

Title

The joint mortality of couples in continuous time

This paper introduces a probabilistic framework for the joint survivorship of couples in the context of dynamic stochastic mortality models. In contrast to previous literature, where the dependence between male and female times of death was achieved using a copula approach, this new framework gives an intuitive and flexible pairwise cohort-based probabilistic mechanism that can accommodate both deterministic and stochastic effects which the death of one member of couple causes on the other. It is sufficiently flexible to allow modeling of effects that are short term (broken heart) or long term in their durations. In addition, it can account for the state of health of the both the surviving and dying spouse and thus can allow for dynamic and asymmetric reactions of varying complexity. Finally, it can accommodate the dependence of lives before the first death. Analytical expressions for bivariate survivorship in representative models are given, and their estimation, done in two stages, is seen to be straightforward. First, marginal survivorship functions are calibrated based on UK mortality data for males and females of chosen cohorts.  Second, the maximum likelihood approach is used to estimate the remaining parameters from simulated joint survival data. We show that the calibration methodology is simple, robust and fast, and can be readily used in practice.

TI 11_3

Keefe, Matthew J.

Title

Objective Bayesian Analysis for Gaussian Improper CAR Models

Choosing appropriate priors for parameters of Bayesian hierarchical models for areal data is challenging. In particular, an improper conditional autoregressive (CAR) component is often used to account for spatial association. The use of vague proper priors for this model requires the selection of suitable hyperparameters. In this talk, we derive objective priors for the Gaussian hierarchical model with an improper CAR component and show that the reference prior results in a proper posterior distribution. We present results from a simulation study to compare properties of the proposed Bayesian procedures. We illustrate our methodology by modeling foreclosure rates in Ohio.

TI 17_2

Kim, Jong-Min

Title

Directional Dependence via Copula Stochastic Volatility Model.

By a theorem due to Sklar in 1959, a multivariate distribution can be represented in terms of its underlying margins by binding them together a copula function. Copulas are useful devices to explain the dependence structure between variables by eliminating the influence of marginals. A copula method for understanding multivariate distributions has a relatively short history in statistics literature; most of the statistical applications have arisen in the last twenty years. In this talk, directional dependence via copula stochastic volatility model will be introduced with real example using financial data.

TI 6_1

Kimberly Sellers

Title

Introducing the Conway-Maxwell-Poisson distribution

The Conway-Maxwell-Poisson (COM-Poisson) distribution is a flexible alternative for modeling count data, and it is quickly growing in popularity in both the statistics and applied quantitative disciplines. While the Poisson distribution maintains the constrained equi-dispersion assumption (where the variance and mean equal), the COM-Poisson distribution allows for data over- or under-dispersion (where the variance is larger or smaller than the mean), and captures three classical distributions as special cases. This talk will introduce the distribution and serve as a review survey for the work done, and a prologue to the subsequent talks in the session.

TI 10_3

Kleiber, Christian

Title

On moment indeterminacy of the generalized variance

The moment problem asks whether a distribution can be uniquely characterized by the sequence of its moments. In the univariate case, counterexamples have been known for decades, e.g., the lognormal and certain generalized gamma distributions. In the multivariate case, knowledge is still much more limited. Here we consider a univariate sampling distribution from classical multivariate analysis, the generalized variance, which leads to a Stieltjes-type moment problem. It is shown that this object is not determined by the sequence of its moments although all the moments are finite. There is a dimension effect: the bivariate case the distribution is moment-determinate, whereas in dimensions greater than two the distribution is moment-indeterminate.

TI 4_3

Li, Pengfei

Title

Controlling IER and EER in replicated regular two-level factorial experiments

Replicated regular two-level factorial experiments are very useful for industry. The goal of these experiments is to identify active effects that affect the mean and variance of the response. Hypothesis testing procedures are widely used for this purpose. However, the existing methods give results that are either too liberal or conservative in controlling the individual and experimentwise error rates (IER and EER). In this paper, we propose a resampling procedure and an exact-variance method to identify active effects for the mean and variance, respectively, of the response. Monte Carlo studies show that our methods control the IER and EER well.

TI 13_2

Madsen, Lisa

Title

Simulating Dependent Count Data

Statisticians simulate data for a variety of purposes: to assess and compare the performance of statistical procedures and to design studies. Therefore, the ability to simulate realistic data is an important tool. I will discuss a method to simulate count-valued dependent random variables from the Gaussian copula that mimic observed data sets. Researchers typically characterize dependence by Pearson's produce-moment correlation, but for small-mean counts, this is not as sensible as other measures such as Spearman's rank correlation. Furthermore, for small-mean count distributions, the high probability of ties requires special attention. I will show how to determine the Gaussian copula correlation matrix that will lead to any specified feasible Spearman or Pearson correlation matrix. I will demonstrate the method with an example based on an actual data set.

TI 9_3

Mailhot, Mélina

Title

Reciprocal Reinsurance Treaties Under an Optimal and Fair Joint Survival Probability

Optimal reinsurance treaties between an insurer and a reinsurer considering both parties' interests will be presented. Most articles only focus on the insurer's point of view. The latest research considering both sides have considerably oversimplied the joint survival function. This situation leads to an unrealistic optimal solution; one of the parties can make risk-free profits while the other bears all the risk. A fair joint survival probability will be defined and optimized for a reciprocal reinsurance treaty under different principles and types of contract.

TI 17_5

Makubate, Boikanyo, Galetlhakanelwe Motsewabagale, Broderick O. Oluyede, Alphonse Amey

Title

Dagum Power Series Class of Distributions with Applications to Lifetime Data

In this paper, we present a new distribution class of distributions called the Dagum-Power Series (DPS) distribution and in particular the Dagum-Poisson (DP) distribution.  This model is obtained by compounding Dagum distribution with the power series distribution. The hazard function, reverse hazard function, moments and mean residual life function are obtained. Methods of finding estimators such as Minimum Distance, Maximum Product of Spacing, Bayesian estimators, Least Squares, Weighted Least Squares and Maximum Likelihood will be discussed. A simulation study will be carried out to compare these estimation methods.  Each method has its own strength and weakness. We also carry out some hypothesis tests using the Wald test statistic. This distribution will be shown to be competitive model for describing censored observations in life time reliability problems. Finally, we apply the Dagum-Poisson distribution to real dataset to illustrate the usefulness and applicability of the distribution.

TI 22_4

Mallick, Avishek

Title

Robustness of Multiple Comparison Methods for One-way and Two-way ANOVA with Repeated Measurements

In many experiments several observations are taken over time or with several treatments applied to each subject. These observations tend to be highly correlated, particularly those observed adjacent to each other with respect to time. In this paper we investigate the effect of the correlations among the observations in one-way and two-way ANOVA. A modification of the standard tests suitable for AR(1) correlation structure is proposed and its properties are investigated. We also apply the approximations to the distribution of F tests as suggested by Andersen, Jensen, and Schou (1981) and carry out the analysis. The modified procedure allows us to have a better control of the nominal significance level α. Consequently, the multiple comparisons and multiple tests based on this modified procedure will lead to conclusions with better accuracy.

TI 4_1

Mandal, Saumen

Title

Optimal designs for minimizing correlations among parameter estimators in a linear model

In many regression designs it is desired to render certain parameter estimators uncorrelated with others. Motivated by this fact, we construct optimal designs for minimizing covariances among the parameter estimators in a linear model, thereby rendering the parameter estimators approximately uncorrelated with each other. In the case of rendering a parameter estimator uncorrelated with another two estimators, we set up a compound optimization problem and transform the problem to one of maximizing two functions of the design weights simultaneously. The approaches are formulated for a general regression model and are explored through some examples including one practical problem arising in Chemistry.

TI 19_4

McNicholas, Paul

Title

Mixture of Coalesced Generalized Hyperbolic Distributions

A mixture of multiple scaled generalized hyperbolic distributions (MSGHDs) is introduced. Then, a mixture of coalesced generalized hyperbolic distributions is developed by joining a finite mixture of generalized hyperbolic distributions with a MSGHD. After detailing the development of the mixture of MSGHDs, which arises via implementation of a multi-dimensional weight function, the density of the coalesced distribution is developed. A parameter estimation scheme is developed using the ever-expanding class of MM algorithms and the Bayesian information criterion is used for model selection. The issue of cluster convexity is examined and a special case of the MSGHDs is developed that is guaranteed to have convex clusters. These approaches are illustrated and compared using simulated and real data.

TI 6_4

Morris, Darcy S.

Title

Bivariate Conway-Maxwell-Poisson Distribution: Formulation, Properties, and Inference

The bivariate Poisson distribution is a popular distribution for modeling bivariate count data.  Its basic assumptions and marginal equidispersion, however, may prove limiting in some contexts.  To allow for data dispersion, we developed a bivariate Conway-Maxwell-Poisson (COM-Poisson) distribution that includes the bivariate Poisson, bivariate geometric, and bivariate Bernoulli distributions all as special cases. As a result, the bivariate COM-Poisson distribution serves as a flexible alternative and unifying framework for modeling bivariate count data, especially in the presence of data dispersion. This is joint work with Kimberly Sellers (Georgetown University) and Narayanaswamy Balakrishnan (McMaster University).

TI 20_3

Moura, Ricardo

Title

Likelihood-based exact inference for Posterior and Fixed-Posterior Predictive Sampling synthetic data under the MLR model

Synthesizing datasets as a Statistical Disclosure Control technique has become more and more popular.  Under multivariate linear regression model, likelihood-based exact inference for singly and multiply imputed synthetic data generated under Posterior Predictive Sampling (PPS) will be presented, filling a gap in the existing SDC  literature. It will be also presented a likelihood-based exact inference for multiply imputed data generated via a new method, called Fixed-Posterior Predictive Sampling (FPPS), proposed to overcome problems inherent to the PPS method. An application using U.S. 2000 Current Population Survey data will be discussed and comparisons between PPS and FPPS are presented.

TI 3_3

Muthukumarana, Saman

Title

Non-inferiority Hypothesis Testing in Two-arm Trials using Relative Belief Ratios

We discuss a Bayesian approach for assessing non-inferiority in two-arm trials using relative belief ratio. A relative belief ratio is a measure of the evidence in favour of a hypothesis. It is similar to the Bayes factor as both measure the change in belief from a priori to a posteriori but has better optimal properties. Under different conditions, we obtain the posterior distribution of the difference in treatment effects between experimental treatment and reference treatment. Once this distribution is determined, we propose a Bayesian decision criterion using the relative belief ratio. We illustrate the proposed method by applying it to data arising from two-arm clinical trials. Some extensions to discrete data with excessive zeros will also be discussed.

TI 21_4

Ng, Hon Keung Tony

Title

Statistical Inference for Component Distribution from System Lifetime Data

In this talk, statistical inference of the reliability characteristics of the components in the system based on the lifetimes of systems will be discussed. We study the problem of testing the homogeneity of distributions of component lifetime based on system lifetime data with known system signatures. Both parametric and nonparametric procedures are developed for this problem. The performance and limitations of the proposed nonparametric method are discussed. Then, we assume the component lifetimes follow exponential distributions and develop exact and asymptotic parametric tests. Monte Carlo simulation study is used to compare the performance of different parametric and nonparametric procedures.

TI 7_4

Nguyen, Christine and Huang Mei Ling

Title

On High Quantile Regression

The estimation of conditional quantiles at very high or low tails of a heavy tailed distribution is of interest in numerous applications. We study a linear quantile regression model which uses an L1- loss function, and the optimal solution of linear program, for estimating coefficients of regression. This paper proposes a weighted quantile regression method for certain extreme value sets. Monte Carlo simulations show good results for the proposed weighted method. Comparisons of the proposed method and existing methods are given. The paper also investigates real-world examples by using the proposed weighted method.

TI 18_3

Nkurunziza, Sévérien

Title

A class of restricted estimators in multivariate measurement error regression model

In this paper, we study an estimation problem in multivariate regression model with measurement error. In particular, we consider the case where the regression coefficient may satisfy some restrictions. We propose the unrestricted estimator (UE) and a class of restricted estimators, which includes as a special cases three restricted estimators given in recent literature. Further, we study the asymptotic properties of the proposed class of estimators under the null and alternative hypothesis. To this end, we generalize some findings underlying the elliptically contoured distributions. Thanks to the generalized findings, we establish Asymptotic Distributional Risk (ADR) for the UE as well as the ADR of any member of the proposed class of the restricted estimators and we compare their relative performance. It is established that near the null hypothesis, the restricted estimators (REs) perform better than the UE. But the REs perform worse than the UE when one moves far away from the null hypothesis. Finally, in order to illustrate the application of the proposed method, we present some simulations and we analyze a real data set. The numerical findings corroborate the established theoretical results.

TI 10_1

Nolde, Natalia

Title

Multivariate light-tailed distributions: from the asymptotic shape of sample clouds to properties of multivariate extremes.

Sample clouds of multivariate data points from light-tailed distributions can often be scaled to converge onto a deterministic set as the sample size tends to infinity. It turns out that the shape of this limit set can be related to a number of extremal tail and dependence properties of the underlying multivariate distribution. In this talk, I will present several simple relations, and illustrate how they can be used to replace frequently cumbersome or intractable analytical computations.

TI 15_3

Oh, Dong Hwan

Title

Time-Varying Systemic Risk: Evidence from a Dynamic Copula Model of CDS Spreads

This paper proposes a new class of copula-based dynamic models for high dimension conditional distributions, facilitating the estimation of a wide variety of measures of systemic risk. Our use of copula-based models enables the estimation of the joint model in stages, greatly reducing the computational burden. We use the proposed new models to study a collection of daily CDS spreads on 100 U.S. firms. We find that while the probability of distress for individual firms has greatly reduced since the 2008 financial crisis, a measure of systemic risk is substantially higher now than in the pre-crisis period.

TI 17_4

Oluyede, Broderick O.

Title

The Burr XII Weibull Power Series Distribution: Theory and Applications

A new class of power series distributions is developed and presented. In particular, the new Burr XII Weibull-Poisson (BWP) distribution is introduced and its properties are explored in detail. Some estimation techniques including maximum likelihood estimation method are used to estimate the model parameters and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed class of distributions.

TI 22_2

Otunuga, Michael

 

Distribution Models of Energy Commodity Spot Price Processes

In this work, we undertake the study to shed light on world oil market and price movement, price balancing process and energy commodity behavior. A system of stochastic model for dynamic of energy pricing process is proposed. Different methods for parameter estimation is discussed. In addition, by developing a Local Lagged Adapted Generalized Method of Moment (LLGMM) method, an attempt is made to compare the simulated estimates derived using LLGMM and other existing method. These developed results are applied to the Henry Hub natural gas, crude oil, coal, and ethanol data set.

TI 8_3

Paolella, Marc

Title

Stable Paretian Distribution Testing

A fast method for estimating the parameters of a stable-APARCH not requiring likelihood or iteration is proposed. Several powerful tests for the (asymmetric) stable Paretian distribution with tail index $1< \alpha < 2$ are developed and used for assessing the appropriateness of the stable assumption as the innovations process in stable-GARCH-type models for daily stock returns. Overall, there is strong evidence against the stable as the correct innovations assumption for all stocks and time periods, though for many stocks and windows of data, the stable hypothesis is not rejected.

TI 22_1

Pararai, Mavis

Title

A New Lifetime Distribution With Applications

The beta Lindley-Poisson (BLP) distribution which is an extension of the Lindley-Poisson Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, hazard rate function, moments and moment generating function, skewness and kurtosis are explored. Renyi entropy and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally applications of the model to real data sets are presented for the illustration of the usefulness of the proposed distribution.

TI 2_3

Peng, Yingwei

Title

Prediction accuracy for cure probability in cure models

Prediction accuracy of a cure model to predict the cure probability of a subject is an important but not well addressed issue in survival analysis. We propose a method to assess the prediction accuracy of a mixture cure model in predicting cure probability based on inverse probability of censoring weights to incorporate the censoring and latent cure status in the data. The consistency of the estimator is examined. A simulation study is conducted to investigate the performance of estimator based on training data only. An application of the method to a real data set is illustrated.

TI 8_2

Pigeon, Mathieu

Title

Composite (mixed) models for individual loss reserving

In this talk, we consider composite models (CM) based on a distribution f up to an unknown threshold and a distribution g thereafter. Instead of using a single threshold value applying uniformly to the whole dataset, a composite mixed model (CMM) allows for heterogeneity with respect to the threshold and let it vary among observations. More specifically, the threshold value for a particular observation is seen as the realization of a random variable and the CMM is obtained by averaging over the population of interest. We apply these models, and some extensions, to evaluate loss reserves in a micro-level actuarial dataset. We illustrate results with an empirical analysis using a real portfolio as well as with simulations.

TI 15_1

Plante, Jean-François

Title

Rank Correlation under Categorical Confounding

Rank correlation is invariant to marginal transformations, but it is not immune to confounding. Assuming a categorical confounding variable is observed, the author proposes weighted coefficients of correlation developed within a larger framework based on copulas. While the weighting is clear under the assumption that the dependence is the same within each group implied by the confounder, the author extends the Minimum Averaged Mean Squared Error (MAMSE) weights to borrow strength between groups when the dependence may vary across them. Asymptotic properties of the proposed coefficients are derived and simulations are used to assess their finite sample properties.

TI 1_3

Prieto, Faustino and Sarabia, Jose Maria

Title

Family of generalized power law (GPL) distributions: Properties and Applications

Many real phenomena can be modelled by the Power Law (Pareto) distribution  in their upper tail. However, that distribution usually fails when we focus on their whole range. In this paper, we provide empirical evidence that, the family of Generalized Power Law (GPL) distributions, can be useful for modelling the whole range, of those real phenomena with power law tail. To do that,  we combine máximum likelihood method, as a fitting technique, with Kolmogorov-Smirnov test method based on bootstrap resampling, as a goodness of fit test. In addition, we compare that  family of distributions with other well known distributions.

TI 8_4

Provost, Serge

Title

Differentiated Logdensity Estimates and Approximants as Rational Functions

We propose a density approximation methodology whereby the derivative of the logarithm of a density approximant is expressed as a polynomial or a rational function. The polynomial coefficients are determined by matching moments and solving the resulting system of linear equations. This methodology is applied to two test statistics as well as certain mixtures of density functions. As well, it is explained that this approach can produce density estimates.

TI 6_2

Raim, Andrew

Title

A flexible zero-inflated model to address data dispersion

The Conway–Maxwell–Poisson distribution has seen increased interest in recent years due to its ability to model both overdispersion and underdispersion relative to the Poisson distribution. This work considers a zero-inflated Conway–Maxwell–Poisson (ZICMP) distribution for the common problem of excess zeroes in count data. ZICMP becomes a flexible regression model by linking covariates to its count rate and zero-inflation parameters. Through simulation, we examine some properties of the maximum likelihood estimator and a test for equidispersion. ZICMP performs favorably compared to related count models in analyzing several synthetic datasets, as well as a real study of unwanted pursuit behaviors in separated couples.

TI 8_1

Ren, Jiandong

Title

Moment-Based Density Approximations for Aggregate Losses

The determination of the distribution of aggregate losses is of crucial importance for an insurer. We apply a moment-based density approximation method to approximate the distributions of univariate and bivariate aggregate losses. The proposed technique which is conceptually simple and computationally efficient, constitutes a viable alternative to the commonly used recursive and FFT methods. As well, given a set of observed aggregate losses, the methodology advocated herein can readily be applied in conjunction with the sample moments for modeling purposes.

TI 10_4

Richter, Wolf-Dieter

Title

Statistical reasoning on scaling parameters in dependent p-generalized elliptically contoured distributions

Scaling parameters of two dependent variables having known expectations are compared if the two-dimensional observation vector follows a p-generalized elliptically contoured distribution. Basic properties of the geometric representation of the multivariate sample distribution are used in constructing exact significance tests and confidence estimates.

TI 1_1

Saez-Castillo, Antonio Jose and Conde-Sanchez, Antonio

Title

Regression models based on extended Poisson distributions in R

Many discrete probability distribution has tried to extend the Poisson distribution and solve the problem of lack of equidispersion, mainly due to the presence of individual heterogeneity, but also caused by the existence of negative contagion effect. Only a reduced subset of these extended Poisson distributions has been employed to develop regression models for count data. In this work, we present a survey of such models which have been implemented in R Statistical Software. Code to describe applications in Business, Management and Economics is included and commented to facilitate their use.

TI 15_2

Samanthi, Ranadeera

Title

Comparing the Riskiness of Dependent Insurance Portfolios

A nonparametric test based on nested L-statistics to compare the riskiness of portfolios was introduced by Brazauskas, Jones, Puri, and Zitikis (2007). In this work, we investigate how the performance of the test changes when insurance portfolios are dependent. To achieve that goal, we perform a simulation study using spectral risk measures. Further, three insurance portfolios are generated, and their interdependence is modeled with the three-dimensional elliptical copulas. It is found that the presence of comonotonicity makes the test liberal for all the risk measures under consideration. We illustrate how to incorporate such findings into sensitivity analysis of decisions.

TI 1_4

Sarabia, Jose Maria and Prieto, Faustino

Title

A Hierarchy of Multivariate Pareto Distributions with Applications in Risk Analysis

The Pareto distribution and all its different versions have long been used as a suitable model for many non-negative economic variables, including losses and other variables in risk analysis. In this paper we introduce a hierarchy of multivariate Pareto distributions. The hierarchy is composed by three families, which permits more and more flexibility. We consider the aggregated risks and we study the individual and collective risk models based on the three dependence structures. In two of these families we consider some relevant collective models with Poisson and negative binomial as primary distributions.  Finally, some applications with data are given.

TI 7_2

Sclove, Stanley

Title

Extreme Values or Mixture Distribution?

For modeling a dataset of employee days ill, or accidents among insureds, levels of granularity are considered in describing the population, from a single distribution, possibly with extreme values, to a bimodal distribution, to a mixture of two or more distributions, to modeling the population at the individual level.

TI 16_3

Shahtahmassebi, Golnaz

Title

Bayesian Estimation of Change Point problems using Conditionally Specified Prior Distributions with Applications

In data analysis, change point problems correspond to abrupt changes in stochastic mechanisms generating data. The detection of change points is a relevant problem in the analysis and prediction of time series. In this talk, we propose and illustrate a Bayesian solution to the estimation of change point problems. The estimation is based on a broad class of conjugate prior distributions constructed from a conditional specification methodology. Hyperparameter elicitation methodologies are discussed and simulation from the resulting posterior distributions is obtained using Gibbs sampler. We demonstrate some examples with simulated and real data.

TI 4_2

Sinha, Sanjoy

Title

Joint modeling of longitudinal and survival data with a covariate subject to limit of detection

Joint models are often used for investigating the effect of an endogenous time-dependent covariate on survival times. I will discuss a novel method for jointly analyzing longitudinal and time-to-event data when a covariate is subject to the limit of detection. We often assume latent processes based on random effects in order to describe the association between longitudinal and time-to-event data. We study the effects of misspecified random effects distributions on the estimates of the model parameters. We also present an application of the proposed method using a large clinical dataset.

TI 21_3

So, Hon Yiu

Title

Title of Presentation: The EM algorithm for One-shot Device Testing with Competing Risk under Different Lifetimes Distributions

In this talk, we extend the recent works of Balakrishnan and Ling by introducing a competing risk model into a one-shot device testing analysis under accelerated life test setting. Expectation maximization (EM) algorithms are developed for the estimation of model parameters under di_erent lifetime distributions. Extensive Monte Carlo simulations are carried out to assess the performance of the proposed method of estimation. The advantages of the EM algorithms over the traditional Fisher scoring method are displayed through simulation.

TI 13_3

Song, Peter

Title

Copula Random Field with Application to Longitudinal Neuroimaging Data Analysis          

Motivated by the needs of analyzing massive longitudinal imaging data, we present an extension of GeoCopula proposed by Bai et al. (2014). This new model, termed as imageCopula, helps us to address multilevel spatial-temporal dependencies arising from longitudinal imaging data. We propose an efficient composite likelihood approach by constructing joint composite estimating equations (JCEE) and develop computationally feasible algorithm to solve the JCEE. We show that the computation is scalable to large-scale imaging data. We conduct several simulation studies to evaluate the performance of the proposed models and estimation methods. We apply the imageCopula to analyze a longitudinal PET data set from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

TI 5_1

Su, Steve

Title

Transformation and Family of Generalised Lambda Distributions

Generalised lambda distributions (GLDs) are very versatile distributions that can effectively model a wide range of continuous empirical data, despite their simple looking formulae. The versatility of GLDs can be extended further by considering one to one, monotonic transformation of GLD variables to generate new distributions. This presentation discusses the theory, application and fitting algorithm of exponential, arctan, inverse (domain of data being positive or negative, but not both) and squared (positive values only) transformations of GLDs for survival analysis, truncated data and extreme value modelling, and attaining shapes that traditionally can only be achieved using mixtures of statistical distributions.

TI 11_1

Tegge, Allison N.

Title

Bayesian analysis for multi-subject time course RNA-seq experiments

We introduce Bayesian methodology for the analysis of multi-subject time course RNA-seq experiments. Our methodology facilitates the study of gene reactions to certain biological processes through time. Specifically, we develop an empirical Bayes approach to detect differentially expressed genes that reduces the high dimensionality of time course data by empirical orthogonal functions. The proposed model assumes distinct distributions for differentially and non-differentially expressed genes, and borrows strength across genes and subjects to increase detection power. We illustrate our methodology with an analysis of an RNA-seq dataset from B cells to study their temporal response pattern to the human influenza vaccine.

TI 20_2

Teodoro, M. Filomena

Title

Modeling the time between failures using likelihood ratio tests

The aim of this work is to model the time between failures of certain type of equipment essential for the proper functioning  of ships from a certain  class from Portuguese Navy , so  the maintenance can be  adjusted avoiding additional costs. To help us choose among different distributions that may be fitted to these data, we will use likelihood ratio tests for the equality of Gamma distributions. Since the exact distributions of the statistics are not tractable, near-exact distributions will be developed to obtain very sharp p-values and quantiles. This will allow for the easy practical implementation of these tests.

TI 17_3

Tsukahara, Hideatsu

Title

The empirical beta copula

Applying Baker's construction of copulas based on the order statistics with the ranks being coefficients leads us to define the empirical beta copula, which is a particular case of the empirical Bernstein copula. We show that the empirical beta copula is a genuine copula by providing (necessary and) sufficient conditions for a Bernstein transformation to be a copula. Furthermore, we establish the assumptions under which the standard asymptotic results hold for the empirical Bernstein copula.  Our Monte Carlo simulation study shows that the empirical beta copula outperforms the empirical copula in terms of the bias and the integrated mean squared error.

TI 18_1

Vinogradov, Vladimir /Paris, Richard B.

Title

Poisson-Tweedie mixtures: a case study

Poisson-Tweedie mixtures constitute a subclass of the family of Poisson mixtures corresponding to the case where the mixing measure is generated by a member of the power-variance family of distributions with non-negative support. For a specific value of the “power” parameter, such mixtures comprise both an additive exponential dispersion model and a factorial dispersion model, which are characterized by the variance and the dispersion functions, respectively. We concentrate on the former structure illustrating our results by paying attention to Neyman type A distributions. We construct local approximations for Poisson-Tweedie mixtures.

TI 12_2

Wang, Bin

Title

Normalizing next-generation sequencing data via Density Estimation and Binning

Next-generation sequencing (NGS) is widely used in biomedical studies. Normalization is challenging and crucial in NGS gene expression profiling data analysis.  We propose to normalize gene profiles by binning the data and estimating the distributions using three methods: 1) root-unroot algorithm, 2) finite normal mixture model using expectation-maximization algorithm, and 3) fitting generalized lambda distribution. In addition, a novel measure of similarity of the gene profiles is proposed to assess the normalization results and detect differentially expressed genes as well. The proposed methods will be applied to multiple NGS data sets and will be benchmarked with some existing NGS normalization methods.

TI 21_1

Wang, Dongliang

Title

Penalized Empirical Likelihood for the Cox Regression Model

Current penalized regression methods for selecting and estimating regression coefficients in the Cox model are mainly developed on partial likelihood. In this paper, an empirical likelihood method is proposed in conjunction with appropriate penalty function. Asymptotic properties of the resulting estimators, including the consistency, asymptotic normality and the oracle property with respect to variable selection, are theoretically proved. Simulation studies suggest that empirical likelihood is superior to partial likelihood in terms of selecting correct risk factors and reducing estimation error. The well-known primary biliary cirrhosis data set is used to illustrate and compare the empirical likelihood method with existing methods.

TI 2_1

Wu, Changbao

Title

Distribution Theory in Empirical Likelihood for Complex Survey Data

Empirical likelihood has been shown to be a useful tool for handling parameters defined through estimating equations. The use of empirical likelihood for complex survey data, however, encounters various issues for the ``non-standard’’ asymptotic distribution of the empirical likelihood ratio statistics. In this talk, we present some basic distribution theory for two different formulations of the empirical likelihood methods for survey data. We further present results on the posterior distribution of the Bayesian empirical likelihood methods and the related computational issues in Bayesian inference for surveys.

TI 11_2

Wu, Ho-Hsiang

Title

Mixtures of Nonlocal Priors for Variable Selection in Generalized Linear Models

We propose two novel scale mixtures of nonlocal priors (SMNP) for variable selection in generalized linear models. In addition, we develop a Laplace integration procedure to compute posterior model probabilities. We show that under certain regularity conditions the proposed methods are variable selection consistent. Simulation studies indicate that our proposed SMNP-based methods select true models with higher success rates than other existing Bayesian methods. Furthermore, our methods lead to mean posterior probabilities for the true models that are closer to their empirical success rates. Finally, we illustrate the application of our SMNP-based methods with the analyses of two real datasets.

TI 9_2

Wu, Jiang/ Zitikis,Ricardas

Title

Background risk models, two-period economies, and optimal strategies that minimize financial losses

Background risk models, including a myriad of Pareto- and beta-type multivariate distributions, provide a particularly intuitive and fruitful way for modeling dependence in real-life applications. In this talk, we shall discuss one of such applications that concerns decision-making in a  two-period economy when a pivotal decision needs to be made during the first time-period and cannot be subsequently reversed.

TI 12_4

Xie, Yuying

Title

Joint Estimation of Multiple Dependent Gaussian Graphical Models with Applications to Mouse Genomics

Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A motivating example is that of modeling gene expression collected on multiple tissues from the same individual: a multivariate outcome that is affected by dependencies at the level of both the tissue and the whole body, and existing methods that assume independence among graphs are not applicable. To estimate multiple dependent graphs, we decompose the problem into two graphical layers: the systemic layer, which is the network affecting all outcomes and thereby inducing cross-graph dependency, and the category-specific layer, which represents the graph-specific variation. We propose a graphical EM technique that estimates the two layers jointly, establish the estimation consistency and selection sparsistency of the proposed estimator, and confirm by simulation that the EM method is superior to a simple one-step method. Lastly, we apply our graphical EM technique to mouse genomics data and obtain biologically plausible results.

TI 4_4

Xu, Xiaojian

Title

Optimal designs for regression when measurement error is present

Optimal designs for regression have a great impact on the precision of model parameter estimation. Utilizing a D-optimal design may ensure that the joint confidence regions for true model parameters will be as small as possible for a fixed sample size. Moreover, measurement error is often present in the majority of models and should be taken into account when designing an experiment. Considering a simple linear model with possible measurement error in both the response and explanatory variables, we have investigated the properties of exact and approximate Doptimal designs for various cases of variance structure associated with measurement error involved.

TI 20_1

Yagi, Ayaka  and Seo, Takashi

Title

The null distribution of the LRT statistic for mean vectors with monotone missing data

In this talk, we consider the likelihood ratio test (LRT) for a normal mean vector or two normal mean vectors when the data have a monotone pattern of missing observations. For the one-sample and two-sample problems, we derive the modified likelihood ratio test statistics by using the asymptotic expansion approximation. Further, we investigate the accuracy of the upper percentiles of these test statistics by Monte Carlo simulation.

TI 2_4

Yi, Grace Y.

Title

Analysis of High-Dimensional Correlated Data  in the Presence of Missing Observations and Measurement Error

In contrast to extensive attention on model selection for univariate data, research on correlated data remains relatively limited. Furthermore, in the presence of missing data and/or measurement error, standard methods would typically break down. To address these issues, we propose marginal methods that simultaneously carry out model selection and estimation for high-dimensional correlated data which are subject to missingness and measurement error. To justify the proposed methods, we provide both theoretical properties and numerical assessments.

TI 18_2

Yu, Guan

Title

Sparse Regression for Block-missing Multi-modality Data

In modern scientific research, many data are collected from multiple modalities (sources or types). Since different modalities could provide complementary information, sparse regression methods using multi-modality data could deliver better prediction performance. However, one special challenge for using multi-modality data is related to missing data. In practice, the observations of a certain modality can be missing completely, i.e., a complete block of the data is missing. In this paper, we propose a new two-step sparse regression method for block-missing multi-modality data. In the first step, we estimate the covariance matrix. Rather than deleting samples with missing data or imputing the missing observations, the proposed method makes use of all available information. In the second step, based on the estimated covariance matrix, a Lasso-type estimator is used to deliver a sparse estimate of the regression coefficients in the linear regression model. The effectiveness of the proposed method is demonstrated by theoretical studies, simulated examples, and a real data example from the Alzheimer’s Disease Neuroimaging Initiative. The comparison between the proposed method and some existing methods also indicates that our method has promising performance.

 

General-Invited Session: Topics and Session Chairs

Session Name: TI m_k (m_k =  kth speaker in the mth session)

Room Abbreviation: NI – Niagara Room, BR - Brock Room, EL – Elisabeth Room, CAN/B – Canadian Room/B

Session

Topic

Session Chair

Date

Time

Room

GI 1

Modeling 1 - Life Time, Biostatistics

Pararai, Mavis 

Oct 15

10:50 am - 12:05 pm

NI

GI 2

High Dimension Data Analysis

Amezziane, Mohamed 

Oct 15

10:50 am - 12:05pm

BR

GI 3

Bayesian 1 , Spatial

Samanthi, Madhuka 

Oct 15

10:50 am - 12:05 pm

EL

GI 4

Other - Miscellaneous

Sepanski, Steve 

Oct 15

10:50 am - 12:05 pm

CAN/B

GI 5

Generalized Distributions 1

Pararai, Mavis 

Oct 15

4:30 pm -5:45 pm

NI

GI 6

Inference -Estimation, Testing

Amezziane, Mohamed

Oct 15

4:30 pm -5:45 pm

BR

GI 7

Modeling 2 -Estimation

Samanthi, Madhuka

Oct 15

4:30 pm -5:45 pm

EL

GI 8

Reliability, Risk

Daniels, John 

Oct 15

4:30 pm -5:45 pm

CAN/B

GI 9

Bayesian 2: Estimation, Model

Cheng, Chin-I

Oct 16

10:50 am – 12:05 pm

BR

GI 10

Generalized Distributions 2

Cooray, K.

Oct 16

10:50 am – 12:05 pm

EL

 

 

Abstracts for General-Invited Speakers (Alphabetic Order)

Session Name: GI m_k (m_k =  kth speaker in the mth session)

GI 4_4

Abdelrazeq, Ibrahim

Title

Goodness-of-Fit Test: Levy Driven Continuous ARMA Model

The Levy driven CARMA(p,q) process is becoming a popular one with which to model stochastic volatility. However, there has been little development of statistical tools to verify this model assumption and assess the goodness-of-_t of real world data (Realized

Volatility). When a Levy driven CARMA(p,q) process is observed at high frequencies, the unobserved driving process can be approximated from the observed process. Since, under general conditions, the Levy driven CARMA(p,q) process can be written as a sum of p-dependent Levy driven Ornstein-Uhlenbeck processes, the methods developed in Abdelrazaeq et al. (2014) can be employed in order to use the approximated increments of the driving process to test the assumption that the process is Levy-driven. Performance of the test is illustrated through simulation assuming that the model parameters are known.

GI 10_1

Aljarrah, Mohammad

Title

Exponential-Normal distribution

In this paper, a new three parameter distribution called the exponential-normal distribution is defined and studied. Various properties of the distribution such as hazard function, quantile function, moments, Shannon entropy are discussed. The method of maximum likelihood is proposed to estimate the parameters of the distribution. A real data set is applied to illustrate the flexibility of the distribution.

GI 10_2

Alshkaki, Rafid S.

Title

An Extension to the Zero-Inflated Generalized Power Series Distributions

In many sampling involving non negative integer data, the zeros are observed to be significantly higher than the expected assumed model. Such models are called zero-inflated models, and are recently cited in literature in various fields of science including; engineering, natural, social and political sciences. The class of zero-inflated Generalized Power Series distributions was recently considered and studied due to its empirical needs and application. In this paper an extension to class of zero-inflated power series distributions was introduced, and its characteristics were studied and analyzed.

GI 10_3

Alzaghal, Ahmad 

Title

The Exponentiated Gamma-Pareto Distribution, Properties and Application

A new distribution, the exponentiated gamma-Pareto distribution is introduced and studied. Some of its properties, including distribution shapes, limit behavior, hazard function, Rényi and Shannon entropies, moments, and deviations from the mean and median are discussed. The method of maximum likelihood is used to estimate the exponentiated gamma-Pareto distribution parameters and a simulation study is carried out to assess its performance. The flexibility of the exponentiated gamma-Pareto distribution is illustrated by applying it to real data sets and the results compared with other distributions.

GI 7_5

Arowolo,  Olatunji and Ayinde, Kayode

Title

Parameter estimation techniques of simultaneous equation model with multicollinearity problem

Multicollinearity problem is still inevitable in Simultaneous Equation Model (SEM). The work adopted the single equation estimators for handling multicollinearity, Ordinary Ridge Regression Estimator (ORRE) and Generalized Ridge Regression Estimator (GRRE) into SEM and proposed some estimators using the approach of the conventional ones.  Monte Carlo experiments were conducted with two (2) types of exogenous variable at seven (7) levels of multicollinearity, correlation between error terms and sample sizes.  The estimators were compared and ranked on the basis of their performances vis-à-vis their finite sampling properties. The proposed estimators, ORR-GRRE, 2SGRRE and OLS-GRRE, are recommended for parameters’ estimation of SEM.

GI 1_5

Bakar, Shaiful Anuar Abu

Title

Actuarial loss modeling with the composite models and its computer implementation

Composite model is a statistical distribution model made by piecing together two distributions at a certain threshold. It increasingly deems attention in actuarial loss modelling. In this study, we propose several variations of the composite model in which Weibull distribution is assumed up to the threshold and a family of Beta distribution beyond it. We also specify two of the composite model parameters in term of other parameters of the model which in turn reduce the number of parameters and form a general construction rule for any two arbitrary distributions. The significance of such approach is further demonstrated with respect to computer implementation in R programming language. Finally the performance of the models is assessed via application to real loss data sets using information criteria based approach.

GI 1_4

Bayramoglu , Konul Kavlak

Title

The mean wasted life time of a component of system

A reliability inspection model in which a component of a technical system has lifetime X and inspection time S is considered. It is assumed that X and S are random variables with absolutely continuous joint distribution function F_(X,S)  and the joint probability density function f_(X,S). Firstly, we consider mean residual life function of the component under two different setups of inspection. Secondly, we consider an inspection model where at the inspection time the component is replaced with its spare regardless of whether the component is alive or failed at this time. Under condition that 0 < t < S < X we are interested in expected value of X - S, which is the mean wasted time of intact at time t component in the case if it will not be failed at inspection time, but will be replaced with the new one. Formula for mean wasted life time expressed in terms of f_(X,S)  and partial derivatives of F_(X,S)  is derived. Some examples with graphical representations are also provided.

GI 4_2 

Bingham, Melissa

Title

Quantifying Spread in 3-D Rotation Data: Comparison of Nonparametric and Parametric Techniques

A measure of spread for 3-D rotation data, called the average misorientation angle, is introduced and bootstrapping will be used to develop confidence intervals for this measure. Existing parametric inference methods for estimating spread in 3-D rotations for the von Mises Uniform Axis-Random Spin and matrix Fisher distributions are then compared to the bootstrapping procedure through a simulation study.  Based on the results on the simulation study, it is determined when the nonparametric or parametric techniques are preferred for different scenarios.

GI 3_1 

Boulieri, Areti

Title

A Bayesian detection model for chronic disease surveillance: application to COPD hospitalisation data

Disease surveillance is an important public health practice, as it provides information which can be used to make successful interventions. Innovative surveillance systems are being developed to improve investigation of outbreaks, with the Bayesian models attracting a lot of interest.  In this work, we propose an extension of a Bayesian hierarchical model introduced by Li et al.(2012), which is able to detect areas with an unusual temporal trend, and a simulation study is carried out to assess the performance of the model. The method is illustrated by application to chronic obstructive pulmonary disease (COPD) hospitalisation data in England at clinical commissioning group (CCG) level, from April 2010 to March 2011.

GI 9_5

Chacko, Manoj

Title

Bayesian density estimation using ranked set sample when ranking is not perfect

In this paper, we consider a ranked set sampling in which an auxiliary variable X is used to rank the sample units. A Bayesian method for estimating the underlying density function of the study variate Y using ranked set sample is proposed when measurement of Xs are also available along with Ys. A Markov chain Monte Carlo procedure is developed to obtain the Bayesian estimator of the density function of Y by assuming a parametric distribution for (X,Y), with the distribution of the parameters having a Dirichlet process prior. A simulation study is used to evaluate the performance of the proposed method.

GI 3_4

Daniels, John

Title

Variogram Fitting Based on the Wilcoxon Norm

Within geostatistics research, estimation of the variogram points has been examined, particularly in developing robust alternatives. The fit of these variogram points, which eventually defines the kriging weights, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination, the non-weighted Wilcoxon outperforms weighted Least Squares.

GI 8_4

Doray, Louis G.

Title

The Double Pareto Lognormal Distribution with Covariates and its Applications in Finance and Actuarial Science

We describe the double Pareto-lognormal distribution, present some new properties and show how the model can be extended by introducing  explanatory variables. First, the double Pareto-lognormal distribution is built from the normal-Laplace distribution and some of its properties presented. The parameters can be estimated by using the method of moments or maximum likelihood. Next, explanatory variables are added to the model by using the mean of the normal distribution. The procedure of estimation for this model is also discussed. Finally, examples of application of the model in finance and fire insurance are illustrated and some useful statistical tests are conducted.

GI 7_4

El Ktaibi, Farid

Title

Change point detection for stationary linear models and MBB applications

The problem of structural stability in a time series environment is a classical problem in statistics. In this presentation, we analyze the detection problem of a change in the marginal distribution of a stationary linear process using MBB techniques. Our model will incorporate simultaneously any change in the coefficients and/or the innovations of the linear process. Moreover, the change-point can be random and data dependent. Our results hold under very mild conditions on the existence of any moment of the innovations and a corresponding condition of summability of the coefficients. Lastly, the performance of our approach is demonstrated through simulations.

GI 2_4

Faisal, Shahla

Title

Improved Nearest Neighbors Imputation for High-Dimensional Longitudinal Data

Longitudinal data often comes with missing values. These values cannot be ignored as it can result in loss of important information regarding samples. Therefore imputation is a good strategy to overcome this problem. In this paper, we present a single imputation method based on weighted nearest neighbors that uses the information from other variables to estimate the missing values. These neighbors use the information from within the sample whose response is measured at different time points and between samples. The simulation results show that the suggested imputation method provides better results with smaller imputation errors.

GI 5_2

Ferrari, Silvia L. P.  and Fumes, Giovana

Title

Box-Cox symmetric distributions and applications to nutritional data

We introduce and study the Box-Cox symmetric class of distributions, which is useful for modeling positively skewed, possibly heavy-tailed, data. The new class of distributions includes the Box-Cox t, Box-Cox Cole-Green, Box-Cox power exponential distributions, and the class of the log-symmetric distributions as special cases. It provides easy parameter interpretation, which makes it convenient for regression modeling purposes.

Additionally, it provides enough flexibility to handle outliers. The usefulness of the Box-Cox symmetric models is illustrated in a series of applications to nutritional data.

GI 8_1

Gleaton, James

Title

Characteristics of Generalized Log-Logistic Families of Lifetime Distributions and Asymptotic  Properties of Parameter Estimators

A brief overview of the generalized log-logistic (GLL) transformation (also called the odd log-logistic transformation) group and the characteristics of lifetime distributions generated using this type of transformation is presented.  It is shown that, for a baseline distribution in an exponential class, the MLE’s for parameters of an exponentiated exponential-class (EE) distribution are jointly asymptotically normal and efficient.  A representation of the GLL-exponential-class density as a series in which each term is proportional to an EE density is developed.  Work on the asymptotic properties of the MLE’s for the GLL-exponential-class distribution is in progress.

GI 10_5

Godbole, Anant

Title

Statistical Distributions in Combinatorics:  Moving from Intractability to Tractability

In this talk, we will present several examples of problems from combinatorics for which the entire distribution of a key variable X is of interest in its own right to distribution theorists, beyond the point probability P(X=0), which is often the primary concen of combinatorialists.  The distributions are either impossible to write in closed form, or available in an intractable closed form.  The Stein-Chen method of Poisson approximation can be used however, to yield Poisson estimates together with error bounds.

GI 5_1

Hodge, Miriam

Title

Comparison of liquefaction data:  An application of a logistic normal distribution in the simplex sample space

Liquefaction occurs when an earthquake liquefies water saturated soil and ejects it to the surface of the soil. This physical process is not well understood. We address this uncertainty with a novel model selection strategy to evaluate models which include: ejecta originate from a combination of multiple layers of sediment; the source sediment layer changed during ejection process; the source sediment layer could be deeper than the candidate samples. The data are logistic normal and comprised of percentages of 120-plus grain size ranges. Compositional analysis in the simplex space identified ejecta origins and the result is confirmed by qualitative analysis.

GI 4_3

Hoshino, Nobuaki

Title

On the marginals of a random partitioning distribution

Kolchin’s model is a class of random partitioning distributions of a positive integer, which includes the celebrated Ewens distribution. This type of distributions defines the joint probability of the frequencies of frequencies, but the marginal distribution of the frequency of a given frequency is not straightforward to derive because of its combinatorial nature. This talk motivates the derivation of such a marginal distribution, and shows two methods: the first one inverts factorial moments, and the second one exploits a fact that Kolchin’s model is the product of some conditional distributions.

GI 5_3

Hristopulos, Dionissios T.

Title

A probability distribution function for finite-size systems with renormalized weakest-link behavior

We investigate weakest-link scaling in systems with complex interactions expressed as ensembles of representative volume elements (RVEs).  The system survival probability function is expressed in terms of inter-dependent RVEs using a product rule. For a finite number of RVEs, we propose the κ-Weibull distribution.  We discuss properties of the κ-Weibull and present results from the analysis of experimental data and simulations pertaining to the return interval distributions of seismic data and of avalanches in fiber bundle models.  Areas of potential applications involve the fracture strength of quasibrittle materials, precipitation, wind speed, and earthquake return times.

GI 3_2

Huang, Hsin-Hsiung

Title

New Mixed Gaussian Affine-Invariant Bayesian Clustering Method

We develop a clustering algorithm which does not requires knowing the number of clusters in advance as well as it is rotation-, scale- and translation-invariant coordinatewise. A highly efficient split-merge Gibbs sampling algorithm is proposed. Using the Ewens sampling distribution as prior of the partition and the profile residual likelihoods of the responses under three different covariance matrix structures, we a posterior distribution on partitions. Our experimental results indicate that the proposed method outperforms other competing methods. In addition, the proposed algorithm is irreducible and aperiodic, so that the estimate is guaranteed to converge to the posterior distribution.

GI 6_4

Jiang, Jiancheng

Title

A new diversity estimator

The maximum likelihood estimator (MLE) of Gini-Simpson's diversity (GS) index is widely used but suffers from large bias when the number of species is large relative to the sample size. We propose a new estimator of the GS index and show its unbiasedness. Asymptotic normality of the proposed estimator is established when the number of species in the population is finite and known, finite but unknown, and infinite. Our theory demonstrates that the proposed estimators share the same efficiency as the MLE for finite and known number of species and is more efficient than the MLE for other situations. Simulations demonstrate advantages of our estimators over the MLE, and an example for the extinction of dinosaurs endorses the use of our approach.

GI 5_5

Jureckova, Jana

Title

Specifying the tails of a distribution

The first question induced by observed data is whether they are governed by a heavy or light tailed probability distribution. Such decision is not always straightforward.  When a specific test rejects the Gumbel hypothesis of exponentiality  of the tails, we do not have an information how heavy is really the distribution. Instead of that, we can rather verify the hypothesis whether the tails of a distribution are heavier than a specific level, measured by the Pareto index. We will discuss some nonparametric tests of this hypothesis and compare them with the parametric likelihood ratio test on the parameters of generalized Pareto distribution. The nonparametric tests use the specific behavior of some sample statistics coming from a heavy-tailed distribution; this is of independent interest and can be extended e.g. to AR time series. While the parametric test behaves better when the data really come from a generalized Pareto distribution, the nonparametric tests are typically better for other cases.

GI 8_2

Karlis, Dimitris

Title

On mixtures of multiple discrete distributions with application

In this paper we present a model to fit appropriately data with a lot of periodic spikes in certain values. The motivation comes from a dataset on the number of absence from work. The data show clearly spikes in certain days, implying the different scale of doctor decisions. A new modeling approach, based on finite mixtures of multiple discrete distributions of different multiplicities, is proposed to fit this kind of data.  Multiple Poisson and negative binomial distributions are defined and used for modeling. A numerical application with a real dataset concerning the length, measured in days, of inability to work after an accident occurs is treated. The main finding is that the model provides a very good fit when working week, calendar week and month multiplicities are taken into account. Properties of the derived model are examined together with estimation and inference.

GI 6_1

Lewin, Alex

Title

Fuzzy multiple testing procedures for discrete test statistics

Commonly used multiple testing procedures controlling the Family Wise Error Rate or the False Discovery Rate can be conservative when used with discrete test statistics. We propose fuzzy multiple comparison procedures which give a fuzzy decision function, using the critical function of randomised p-values. We also define adjusted p-values for the new multiple comparison procedures. The method is demonstrated on four data sets involving discrete statistics. A software package for the R language is available.

GI 7_1

Liu, Sifan and Xie, Min-ge

Title

Exact Inference on Meta-Analysis with Generalized Fixed-Effects and Random-Effects Models

For meta-analysis with fixed-effects and random-effects models, conventional methods rely on Gaussian assumptions and/or large-sample approximations. However, when the number of studies is not large, or the sample sizes of individual studies are small, such assumptions and approximations may be inaccurate and lead to invalid conclusions. In this talk, we will present "exact'' confidence intervals for the overall effect using all available data. Our proposals cover generalized models without Gaussian assumptions, and there is no need of approximation. Confidence distribution interpretations and numerical studies, including quantifying the efficacy of BCG vaccine against tuberculosis, will be given for illustrations.

GI 1_3

Mandrekar, Jay

Title

Statistical approach for the development, prediction, and validation of a simple risk score: application to a neurocritical care study.

Patients admitted to neurocritical care units often have devastating neurologic conditions and are likely candidates for organ donation after cardiac death. Improving our ability to predict the time of death after withdrawal of life-sustaining measures could have significant impact on rates of organ donation after cardiac death and allocation of appropriate medical resources. In the first part of the presentation, we will discuss using logistic regression and ROC analysis how we arrived at a prediction model based on a retrospective database. Next, we will discuss the validation of model and development of score using data from a multicenter prospective study.

GI 9_4

Maruyama, Yuzo

Title

Harmonic Bayesian prediction under alpha-divergence

We investigate Bayesian shrinkage methods for constructing predictive distributions. We consider the multivariate Normal model with a known covariance matrix and show that the Bayesian predictive density with respect to Stein's harmonic prior dominates the best invariant Bayesian predictive density, when the dimension is not less than three. Alpha-divergence from the true distribution to a predictive distribution is adopted as a loss function.

GI 1_1

Matheson , Matthew

Title

The Shape of the Hazard Function: The Generalized Gamma and Its Competitors

A large number of distributions have been proposed for parametric survival analysis. The generalized gamma, with its flexible taxonomy of four distinct hazard shapes and ease of implementation, has proven to be one of the most popular. In search of distributions with potentially richer hazard behavior, we have investigated the exponentiated Weibull, generalized Weibull, and beta-generalized gamma using both real and simulated data. Somewhat surprisingly, these distributions appear unable to significantly improve on the flexibility of the generalized gamma for applications, with the generalized gamma being able to closely match almost any parameter combination of the other three distributions.

GI 4_1

Mi, Jie

Title

Instant System Availability

In this talk, we study the instant availability A(t) of a repairable system using integral equation. We have proved initial monotonicity of the availability, and derived various lower bounds of A(t) and average availability. The availabilities of two systems are also compared with the help of stochastic ordering.

GI 8_3

Minkova, Leda

Title

Distributions of order K in risk models

The most used generalization of the counting process in the Risk model is a compound Poisson process. In this talk a counting process with distributions of order K is given. At first we introduce the compound birth process of order K.  As a particular case we consider the compound Poisson process. As examples, the Poisson process of order K, and two types of Polya-Aeppli processes of order K are given. Some functions related to corresponding risk models are analyzed. The derivation of the joint distribution of the time to ruin and the deficit at ruin as well as the ruin probability are given. We discuss in detail the particular case of exponentially distributed claims.

GI 10_4

Nolan, John

Title

Classes of generalized spherical distributions

A flexible class of multivariate generalized spherical distributions with star-shaped level sets is developed.  Tools from computational geometry and multivariate integration are used to work with dimension above two.  The R package gensphere allows one to compute multivariate densities and simulate from such distributions.

GI 4_5

Ozturk, Omer

Title

Ratio estimators based on ranked set sampling in survey sampling

In this talk, we consider the ratio estimator in a finite population setting in a ranked set sampling (RSS) design when the sample is constructed without replacement. We show that the proposed ratio estimator is slightly biased, but the amount of bias is smaller than the bias of the simple random sample (SRS) ratio estimator.  We provide an explicit expression for the approximated mean square error of the ratio estimator and for its precision relative to other competing estimators. We show that the new estimator has substantial amount of improvement in efficiency with respect to SRS estimator. We apply the proposed estimator to estimate apple production in Marmara Region of Turkey in a finite population setting.

GI 3_5

Paul, Rajib

Title

Real Time Estimation of ILI (Influenza Like Illnesses) Rates Using Dynamic Downscaling

Despite novel advances in surveillance of flu trends, the real-time daily estimates of ILI cases are often unavailable. The community health departments collect daily information on reported respiratory and constitutional symptoms (for example, fever, headache, cough etc.). Google flu trends provide weekly estimates per one hundred thousand people. We develop a Bayesian hierarchical model for dynamic downscaling of ILI rates on daily scale fusing these two datasets. We also incorporate environmental factors, such as, temperature and humidity. A sequential Monte Carlo algorithm is developed for faster computation. Our model is tested and validated using Michigan data over the years 2009-2013.

GI 9_2 

Peer Bilal Ahmad

Title

Bayesian analysis of misclassified generalized Power Series distributions under different loss functions

In certain experimental investigations involving discrete distributions external factors may induce a measurement error in the form of misclassification. For instance, a situation may arise where certain values are erroneously reported; such a situation termed as modified or misclassified has been studied by many researchers. Cohen (1960) studied misclassification for Poisson and binomial random variables. In this paper, we discuss misclassification for the more general class of discrete distributions, the generalized power series distributions (GPSD), where some of the observations corresponding to x=c+1; c≥0 are erroneously observed or at least reported as being x=c with probability α. This class includes among others the binomial, negative binomial, logarithmic series and Poisson distributions. We derive the Bayes estimators of parameters of the misclassified generalized power series distributions under different loss functions. The results obtained for misclassified GPSD are then applied to its particular cases like negative binomial, logarithmic series and Poisson distributions. An example is provided to illustrate the results and a goodness of fit test is done using the moment, maximum likelihood and Bayes estimators.

GI 5_4

Pérez-Casany, Marta

Title

Random-Stopped Extreme distributions

The distribution of the maximum (minimum)  of a random number of independent and identically distributed  random variables  is characterized by means of their probability generating function, and a duality property between the two sets of distributions is derived.   These distributions appear in a natural way as data collection mechanisms, similar to the Stopped-sum distributions. When the sample size is geometrically distributed, one obtains the Marshall-Olkin transformation of the sampled distribution as a particular case.  Special attention will be paid to the case where sample size is Poisson distributed, since it is the one with the most practical appeal.

GI 9_1

Ross, Sheldon

Title

Friendship Paradox and Friendship Network Model

The friendship paradox says that "your friends tend to have more friends than you". We explore this paradox and then suggest a model for a friendship network.

GI 2_2

Ruth, David M.

Title

An approach to the multivariate two-sample problem using classification and regression trees with minimum-weight spanning subgraphs

The multivariate two-sample problem is one of continued interest in statistics. Approaches to this problem usually require a dissimilarity measure on the observation sample space; such measures are typically restricted to numeric variables.  In order to accommodate both categorical and numeric variables, we use a new dissimilarity measure based on classification and regression trees. We briefly discuss this new measure and then employ it with a recently-developed graph-based multivariate test.  New improvements to this test are discussed, test performance is examined via simulation study, and test efficacy is investigated using real-world data.

GI 7_2

Schick, Anton

Title

Estimation of the error distribution function in a varying coefficient regression model

This talk discusses estimation of the error distribution function in a varying coefficient regression model. Three estimators are introduced and their asymptotic properties described by uniform stochastic expansions. The first estimator is a residual-based empirical distribution function utilizing an under-smoothed local quadratic smoother of the coefficient function. The second estimator exploits the fact that the error distribution has mean zero. It improves on the first estimator, but is not yet efficient. An efficient estimator is obtained by adding a stochastic correction term to the second estimator.

GI 1_2

Song, Xinyuan

Title

Analysis of proportional mean residual life model with latent variables

In this study, we propose a proportional mean residual life (MRL) model with latent variables to examine the effects of potential risk factors on the MRL function of ESRD in a cohort of Chinese type 2 diabetic patients. The proposed model generalizes conventional proportional MRL models to accommodate latent risk factors. We employ a factor analysis model to characterize latent risk factors via multiple observed variables. We develop a borrow-strength estimation procedure incorporating EM algorithm and the corrected estimating equation approach. The empirical performance of the proposed methodology is evaluated via numerical studies.

GI 6_5

Stehlik, Milan

Title

Exact distributions of LR tests and their applications/Johannes Kepler University Linz, Austria

During the talk we introduce exact statistical procedures based on likelihood ratio. Also practical examples will be given. We introduce exact likelihood ratio tests in exponential family and for a generalized gamma distribution and its properties. We will derive general forms of distributions for exact likelihood ratio test of the homogeneity and scale. Applications and illustrative examples (missing and censored data, mixtures) will be given. Geometry of life time data will be discussed and related to I-divergence decomposition. Small samples testing for frailty through homogeneity test will be discussed. We will provide the methodology for exact and robust test for normality.

GI 3_3

Sun, Ying

Title

A Stochastic Space-time Model for Intermittent Precipitation Occurrences

Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.

GI 2_5

Sylvan, Dana

Title

Exploration and visualization of space-time data with complex structures

We introduce a versatile exploratory tool that may be used to describe and visualize various distributional characteristics of data with complex spatial and spatial-temporal dependencies. We present a flexible mathematical framework for modeling spatial random fields and give possible extensions to space-time data.  For illustration we show applications to air pollution and baseball data.  

GI 6_2

Thomas, Hoben and  Hettmansperger, T.P

Title

Test Scores,  HRX, and Distribution Function Tail Ratios

Let A and D denote advantaged and disadvantaged populations with cdfs $F(x)$ and $G(x)$ respectively, and $F(x) \leq G(x)$. Assume a selection setting; those selected have $x>c$, with $p_A$  and $p_D$ the selected  proportions; $p_D/p_A<<1$. Often the desire is $p_D/p_A\approx 1.$  Consequently  $c$ is lowered.  Surprisingly, the fail ratio $G(c)/F(c)$ and success ratio $[1-G(c)]/[1-F(c)]$ can  both be increasing with decreasing $c$ which Scanlan (2006) calls HRX.  He argues HRX is widely misunderstood, with deleterious public policy results. Conditions for HRX are presented along with data examples.  

GI 9_3

Wang, Min  and Li, Shengnan

Title

Bayesian estimation of the generalized lognormal distribution using objective priors

The generalized lognormal distribution plays an important role in analyzing data from different life testing experiments. In this paper, we consider Bayesian analysis of this distribution using various objective priors for the model parameters. Specifically, we derive expressions for the three types of the Jeffreys priors, the reference priors with different group ordering of the parameters, and the first-order matching priors. We further investigate the properties of the corresponding posterior distributions of the unknown parameter under the various improper priors. It is shown that only two of them result in proper posterior distributions. Numerical simulation studies are conducted to compare the performances of the Bayesian approaches under the considered priors as well as the maximum likelihood estimates. A real-data study is also provided for illustrative purposes.

GI 7_3

Wang, Qiying

Title

Limit theorems for nonlinear cointegrating regression

The past decade has witnessed great progress in the development of nonlinear cointegrating regression. Unlike linear cointegration and nonlinear regression with stationarity where the traditional and classical methods are widely used in practice, estimation and inference theory in nonlinear cointegrating regression produce new mechanisms involving local time, a mixture of normal distributions and stochastic integrals. This talk aims to introduce the machinery of the theoretical developments, providing up-to-date limit theorems for nonlinear cointegrating regression.

GI 2_1

Yu, Chong Ho

Title

Pattern recognition: The role of data visualization and data mining in statistics

Many people say, “Let the data speak for themselves,” yet in higher education the standard curriculum design are still overwhelmingly devoted to hypothesis testing. Although rejecting the null hypothesis based on the p value alone is questionable while there is no detectable pattern in the data, very often data visualization (DV) and data mining (DM) are going unheard among researchers. To rectify this situation, the presenter will show how various DV/DM tools, such as the ternary plot, the diamond plot, the bubble plot, and the GIS map, can be utilized to gain a holistic view of the data patterns.

GI 8_5 

Yu, Jihnhee ; Yang, Luge; Vexler, Albert  and Hutson, Alan D.

Title

Variance Estimation of the Nonparametric Estimator of the Partial Area under the ROC Curve

The pAUC is commonly estimated based on a U-statistic with the plug-in sample quantile, making the estimator a non-traditional U-statistic. In this talk, an accurate and easy method to obtain the variance of the nonparametric pAUC estimator is proposed. The proposed method is easy to implement for both one biomarker test and the comparison of two correlated biomarkers since it simply adapts the existing variance estimator of U-statistics. Further, an empirical likelihood inference method is developed based on the proposed variance estimator through a simple implementation.

GI 2_3

Zahid, Faisal Maqbool  and Heumann, Christian

Title

Multiple Imputation using Regularization

Multiple imputation (MI) is an increasingly popular approach for filling missing data with plausible values. In case of large number of covariates with missing data, existing MI softwares are likely to perform poorly or fail. We are proposing an MI algorithm based on regularized sequential regression models. Each variable (e.g., normal, binary, Poisson etc.) is imputed using its own imputation model. The proposed approach performs well even with large number of covariates and small samples. The results are compared with the existing softwares like mice, VIM, and Amelia in simulation studies. The results are compared using Mean Squared Imputation Error (MSIE) and Mean Absolute Imputation Error (MAIE).


 

Abstracts for Student Posters

(Alphabetically Ordered)

 

All Student Poster Presentations are in Canadian/A Room

The student posters must be posted by 3:00 pm on October 15

The student authors must be at their posters from 5:45 pm – 6:30 pm, October 15

 

Authors

Aldeni, Mahmoud

Title

Families of distributions arising from the quantile of generalized lambda distribution

Statistical distributions play an important role in theory and applications, which are used to fit, model and describe real world phenomena. For this reason, developing new and more flexible univariate statistical distributions has received an increasing amount of attention over the last two decades. In this work, the class of T-R{generalized lambda} families of distributions based on the quantile of generalized lambda distribution has been proposed using the T-R{Y} framework. Different choices of the random variables T and R naturally lead to different families of the T-R{generalized lambda} distributions. Some general properties of these families of distributions are studied. Four members of the T-R{generalized lambda} families of distributions are derived, namely, the uniform-exponential{generalized lambda}, the normal-uniform{generalized lambda}, the Pareto-Weibull{generalized lambda}and the log-logistic-logistic{generalized lambda}. The shapes of these distributions can be symmetric, skewed to the left, skewed to the right, or bimodal. Two real life data sets are applied to illustrate the flexibility of the distributions and the results are compared with the results from some existing distributions.

Authors

Arapis, Anastasios N.

Title

Joint distribution of k-tuple statistics in zero-one sequences

Let a sequence of random variables with values (zero-one) ordered on a line. We consider runs of one of length larger than or equal to a fixed number. The statistics denoting the number of such runs, the number of ones in the runs and the distance between the first and the last run in the sequence, are defined. The paper provides, in a closed form, the exact joint distribution of these three statistics given that the number of such runs in the sequence is at least equal to two. The study is first developed on sequences of independent and identically distributed random variables and then is extended to exchangeable (symmetrically dependent) sequences. Numerical examples illustrate further the theoretical results.   

Authors

Bentoumi, Rachid

Title

Dependence measure under length-biased sampling

In epidemiological studies, subjects with disease (prevalent cases) differ from newly diseased (incident cases). Methods for regression analyses have recently been proposed to measure the potential effects of covariates on survival. The goal is to extend the dependence measure of Kent based on the information gain, in the context of length-biased sampling.  In this regard, to estimate information gain and dependence measure for length-biased data,  we propose to use the kernel density estimation with a  regression procedure . The performances of the proposed estimators, under length-biased sampling, are demonstrated through simulations studies.

Authors

Chaba, Linda and Omolo, Bernard*

Title

Using copulas to select prognostic genes in melanoma patients

We developed a copula model for gene selection that does not depend on the distributions of the covariates, except that their marginal distributions are continuous. A comparison of the ability to control for the FDR of the copula-based model with the SAM and Bayesian models is performed via simulations. Simulations indicated that the copula-based model provided a better control of the FDR and yielded a more prognostic signature than the SAM and Bayesian model-based signatures. These results were validated in three publicly-available melanoma datasets. Relaxing parametric assumptions on microarray data may yield gene signatures for melanoma with better prognostic properties.

Authors

Chan, Stephen

Title

Extreme value analysis of electricity demand in the UK

For the first time, an extreme value analysis of electricity demand in the UK is provided. The analysis is based on the generalized Pareto distribution. Its parameters are allowed to vary linearly and sinusoidally with respect to time to capture patterns in the electricity demand data. The models are shown to give reasonable fits. Some useful predictions are given for the value at risk of the returns of electricity demand.

Authors

Cordero, Osnamir Elias Bru,  Jaramillo, Mario César and Canal, Sergio Yáñez

Title

Random Number Generation for a Survival Bivariate Weibull Distribution

A bivariate survival function of Weibull distribution is presented as Model VI(a)-5 by Murthy, Xie and Jiang. It is shown that the model corresponds to a Gumbel-Hougaard survival copula evaluated at two Weibull survival marginal. Their properties are studied to compare three method of random generation from that distribution. The CD-Vines methodology is used as the base reference for the purpose of methodology evaluation.

Authors

De Silva, Kushani

Title

Bayesian Approach to Profile Gradient Estimation using Exponential Cubic Splines

Reliable profile and profile gradient estimates are of utmost important for many physical models. In most situations, the derivative is either difficult to compute or it is impossible to obtain by direct measurement.  Most importantly, for discrete noisy measurements, the differentiation magnifies the random error buried in the measurements, especially for high-frequency components.  Estimating the derivative from point-wise noisy measurements is well known as an ill-posed problem.  A Bayesian recipe based on a model using exponential cubic spline is implemented to estimate the profile gradient of discrete noisy measurements. The spline model is formulated in the space where the quantity (gradient) to be modeled is continuous, instead of being placed in the data space. The gradient profile is well-determined by the mean value of the posterior distribution calculated using Markov Chain Monte Carlo sampling technique.

Authors

Darkenbayeva, Gulsim

Title

Convergence of some quadratic forms used in regression analysis

We consider convergence in distribution of two quadratic forms arising in unit root tests for a regression with a slowly varying regressor. The error term is a unit root process with linear processes as disturbances. The linear processes are non-causal short-memory with independent identically distributed innovations. Our results generalize some statements from Phillips and Solo (1992).

Authors

Hamed, Duha

Title

T-Pareto family of distributions: Properties and Applications

Six families of generalized Pareto distribution were defined and studied using the T-R{Y} framework will be presented with some of their properties and special cases including the Lorenz and Bonferroni curves. The flexibility of two members of these generalized families namely the normal-Pareto{Cauchy} and the exponentiated-exponential-Pareto{Weibull} distribution are assessed by applying them to a couple of real data sets and comparing their results with other distributions.

Authors

Kang, Kai

Title

Bayesian semiparametric mixed hidden Markov models

In this study, we develop a semiparametric mixed hidden Markov model to analyze longitudinal data. The proposed model comprises a parametric transition model for examining how potential predictors influence the probability of transition from one state to another and a nonparametric conditional model for revealing the functional effects of explanatory variables on outcomes of interest. We propose a Bayesian approach that combines Bayesian P-splines and MCMC methods to conduct the statistical analysis. The empirical performance of the proposed methodology is evaluated via simulation studies. An application to a real-life example is presented.

Authors

Krutto, Annika

Title

Estimation in Univariate Stable Laws

In the study four-parameter stable laws are considered.  The explicit representations for the densities of stable laws in terms of elementary functions are unknown and that complicates the estimation of parameters. All stable laws can be uniquely expressed by their characteristic function. The motivation for this study arises from an estimation procedure based on the empirical characteristic function and known as the method of moments. In this study an amended and more fruitful version of the procedure is proposed, extensive simulation experiments over the parameter space are performed. 

Authors

Mdziniso, Nonhle Channon

Title

Odd Pareto Families of Distributions for Modeling Loss Payment Data

A three-parameter generalization of the Pareto distribution is presented to deal with general situations in modeling loss payment data with various shapes in the density function. This generalized Pareto distribution will be referred to as the Odd Pareto family since it is derived by considering the distributions of the odds of the Pareto and inverse Pareto families. Various statistical properties of the Odd Pareto distribution are provided, including hazard function and moments. Loss payment data is used to illustrate applications of the Odd Pareto distribution. The method of maximum likelihood estimation is proposed for estimating the model parameters.

Authors

Nitithumbundit, Thanakorn

Title

Maximum leave-one-out likelihood estimation for location parameter of unbounded densities

Maximum likelihood estimation of a location parameter fails when the density have unbounded mode. An alternative approach is considered by leaving out a data point to avoid the unbounded density in the full likelihood. This modification gives rise to the leave-one-out likelihood. We propose an expectation/conditional maximisation (ECM) algorithm which maximises the leave-one-out likelihood. Podgórski and Wallin (2015) showed that the estimator which maximises the leave-one-out likelihood is consistent and super-efficient. To investigate other asymptotic properties such as the optimal rate of convergence and asymptotic distribution, we use our proposed algorithm on simulated data sets while also evaluating the accuracy of our estimator.

Authors

Odhiambo, Collins Ojwang

Title

A Smooth Test of Goodness-of-fit for the Weibull Distribution: An Application to an HIV Retention data

In this paper, we propose a smooth test of goodness-of-fit for the two-parameter Weibull distribution. The smooth test described here is a score test that is an extension of the Neyman’s smooth tests. Simulations are conducted to compare the power of the smooth test with three other goodness-of-fit tests for the Weibull distribution against the gamma and the lognormal alternatives. Results show that the smooth tests of order three and four are more powerful than the other goodness-of-fit tests. For validation, we apply the goodness-of-fit procedure to retention data in an HIV care setting in Kenya.

Authors

Selvitella, Alessandro

Title

The Simpson's Paradox in Quantum Mechanics

In probability and statistics, the  \emph{Simpson's paradox} is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, while the reverse trend appears for the aggregate data. In this paper, we give some results about the occurrence of the \emph{Simpson's Paradox} in Quantum Mechanics. In particular, we prove that the \emph{Simpson's Paradox} occurs for solutions of the \emph{Quantum Harmonic Oscillator} both in the stationary case and in the non-stationary case. In the non-stationary case, the \emph{Simpson's Paradox} is persistent: if it occurs at any time $t=\tilde{t}$, then it occurs at any time $t\neq \tilde{t}$. Moreover, we prove that the \emph{Simpson's Paradox} is not an isolated phenomenon, namely that, close to initial data for which it occurs, there are lots of initial data (a open neighborhood), for which it still occurs. Differently fro