Date of Award

2016

Document Type

Open Access Dissertation

Department

Epidemiology and Biostatistics

Sub-Department

The Norman J. Arnold School of Public Health

First Advisor

James Hardin

Abstract

This dissertation is comprised and grounded in statistical theory with an application to solving real world problems. In particular, the development and implementation of multiple score tests under a variety of scenarios are derived, applied, and interpreted. In chapter 2, I propose a score test for independence of the marginals based on Lakshminarayana’s bivariate Poisson distribution. Each marginal distribution of the bivariate model is a univariate Poisson distribution, and the parameters of the bivariate distribution can be estimated using maximum likelihood methods. The simulation study shows that the score test maintains size close to the nominal level. To assess the efficiency of the derived score test, the estimated significance levels and powers of the likelihood ratio and Wald tests are compared. A relevant data set is used to illustrate the application of the bivariate Poisson model and the proposed score test for independence. In chapter 3, two score tests are proposed: one for testing independence based on Sankaran and Nair’s bivariate Pareto distribution and one for testing whether Sankaran and Nair’s parameterization reduces to the more popular bivariate Pareto distribution introduced by Lindley–Singpurwalla. The marginal distributions of both bivariate parameterizations are univariate Pareto II distributions, and the parameters of the bivariate distribution are estimated using numerical methods. The simulation studies show that both score tests maintain a significance level close to the nominal size. To check the efficiency of the derived score tests, the estimated significance levels and powers of the likelihood ratio and Wald tests are also compared. One real world data set is used to illustrate the application of both score tests. In chapter 4, an increasingly popular approach to model the

dependence between random variables via the use of copula functions is explored. A score test for testing independence of response variables is proposed for the specific case where the marginal distributions are known to be Poisson. The simulation study shows the test keeps the significance level close to the nominal one. Similarly, the estimated significance levels and powers of the likelihood ratio and Wald tests are also compared to show our test is numerically stable. A real world data set is used to demonstrate the application of the test.

Rights

© 2016, Roy Bower

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