SCHEDULE

ABSTRACTS

Marginalized Random Effects Models for Multivariate Longitudinal Binary Data
Keunbaik Lee
Biostatistics Program
Louisiana State University Health Sciences Center
New Orleans

Generalized linear models with random effects are often used to explain the serial dependence of longitudinal categorical data. Marginalized random effects models (MREMs) permit likelihood-based estimations of marginal mean parameters and also explain the serial dependence of longitudinal data. In this paper, we extend the MREM to accommodate multivariate longitudinal binary data using a new covariance matrix with a Kronecker decomposition which easily explains both the serial dependence and time specific response correlation. A maximum marginal likelihood estimation is proposed utilizing a Quasi-Newton algorithm with Quasi-Monte Carlo integration of the random effects. Our approach is applied to analyze metabolic syndrome data from the Korean Genomic Epidemiology Study (KGES) for Korean adults.

Cotton Fiber Length Distribution, Part I
Linxiong Li
Mathematics Department
University of New Orleans
New Orleans

Eight cotton samples with a wide range of fiber length are selected and tested on the Advanced Fiber Information System (AFIS) instrument. The measured single fiber length data are used for finding the underlying theoretical distribution of the cotton. The theoretical distribution can be considered as the population distribution of the cotton. It is found that a mixture of two Weibull distributions fits the data very well. Fiber length distribution by number and by weight are discussed separately, and in both cases a mixed Weibull distribution shows a good fit to the data. Numerical comparisons for various parameters between the original distribution from the data and the fitted distribution are presented.

Cotton Fiber Length Distribution, Part II
Rachid Belmasrour
Mathematics Department
University of New Orleans
New Orleans

Eight cotton samples with a wide range of fiber length are selected and tested on the Advanced Fiber Information System (AFIS) instrument. It is found that a mixture of two Weibull distributions with five parameters fits the data very well. Meanwhile it is understood that in practice only the projected fiber length is available and that of the original fiber length (Fibers collected from the clamps) is not. Therefore, it becomes crucial to convert the distribution of projected lengths into that of original fiber lengths, which is exactly the optimal goal of our study. Partial Least Squares (PLS) regression is used to predict the five parameters of the distribution of the original fiber length from the five parameters of the distribution of projected fiber length. It is found that the model based on PLS fits the data well. The numerical analysis for the data and the fitted model are presented.

Stochastic Modeling Of Stream Flow Measurements In The Mississippi And Missouri Rivers
Jonathan Joseph
Mathematics Department
University of New Orleans
New Orleans

To describe patterns in annual peak stream-flow values along the Mississippi and Missouri rivers, I collected data from five sites measured over the past 80+ years using the USGS web resources. From the gathered data, histograms and time series charts are produced. Also, descriptive statistics were calculated and a distribution was fit to the data at each site. Two goodness-of-fit tests were performed to each distribution, one that varies for distribution and the other was the chi-square test. The data from each site was transformed using a Box-Cox transformation and tested for independence. Sites with dependent data values were fit to an autoregressive model. After the models were obtained, an examination of the record values was performed. The number of records in the data from each site was compared to the expected number of record values. Then, an estimation of the 95th percentile of the peak flow rate in 2008 was calculated from the results.

Resilience and Reliability Analysis of P2P Network Systems
Xiaohu Li
Mathematics Department
University of New Orleans
New Orleans

The P2P network is widely used in communication system in recent several years due to the decentralized property. This paper conducts resilience analysis of the P2P network by studying the isolation probability of a single user. Some reliability properties of the available time of a single user are also discussed.

Estimation of a Population Size Through Capture-Mark-Recapture Method: A Comparison of Various Point and Interval Estimators
Xing Yang
Mathematics Department
University of Louisiana at Lafayette
Lafayette

This talk deals with estimation of a fixed population size through capture- mark-recapture method that gives rise to hypergeometric distribution. There are a few well known and popular point estimators available in the literature, but no good comprehensive comparison is available about their merits and demerits. Apart from the available estimators, we propose an empirical Bayes estimator of the population size, and then compare all the point estimators in terms of relative bias and relative mean squared error. Based on our comprehensive numerical results we then rank and recommend the point estimators for practical use. Next, we turn our attention to interval estimation of the population size, which is a more challenging problem. Here we propose two new interval estimators (a) an empirical Bayes highest posterior distribution (HPD) interval; and (b) a frequentist interval estimator based on a parametric bootstrap method. Interestingly, our proposed interval estimators may perform much better than the existing ones depending on sampling proportions. Finally, a real-life data set for a green tree frog population is used as a demonstration for all the methods discussed above. Hopefully this work will help the applied researchers, especially ecologists and environmentalists, in improved population size estimation.

Weighted Likelihood Estimation: Issues and Implications
Ayanendranath Basu
Department of Statistics
Pennsylvania State University

The maximum likelihood method is the cornerstone of classical statistical inference. However, the method is notoriously nonrobust under outliers and model misspecifications for many standard models. Understandably, many of the robust alternatives to maximum likelihood estimation essentially represent attempts to robustify the maximum likelihood method itself. An important subclass of these methods are those where one uses the solutions of weighted likelihood score equations. In this talk we will discuss some different formulations of the weighted likelihood estimation method and discuss their properties.