Physical Sciences and Mathematics Commons^™

Semi-Parametric Likelihood Functions For Bivariate Survival Data, S. H. Sathish Indika

Mathematics & Statistics Theses & Dissertations

Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of …

A Study Of Relationships Between Family Members Using Familial Correlations, Corinne Wilson

Mathematics & Statistics Theses & Dissertations

Familial correlations measure the resemblance between family members and are used in many fields of study including epidemiology, genetics, heredity, and psychology. Here, an analysis of familial correlations where male and female children of the same family can have different correlations in the unequal family size case is presented. First, three likelihood based tests, namely the likelihood ratio test, Rao score test, and Wald test, and two more asymptotic tests which use Srivastava's estimator of the intraclass correlation coefficient are considered to test the null hypothesis of equality of the intraclass correlation coefficients when families have unequal numbers of children. …

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Canonical Correlation Analysis For Longitudinal Data, Raymond Mccollum

Mathematics & Statistics Theses & Dissertations

Data (multivariate data) on two sets of vectors commonly occur in applications. Statistical analysis of these data is usually done using a canonical correlation analysis (CCA). Occurrence of these data at multiple occasions or conditions leads to longitudinal multivariate data for a CCA. We address the problem of canonical correlation analysis on longitudinal data when the data have a Kronecker product covariance structure. Using structured correlation matrices we model the dependency of repeatedly observed data. Recent work of Srivastava, Nahtman, and von Rosen (2008) developed an iterative algorithm to determine the maximum likelihood estimate of the Kronecker product covariance structure …

Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

Mathematics & Statistics Theses & Dissertations

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the …