Candidate: Diana R. Cucos

Degree of: Doctor of Philosophy

Department: Statistics

Title: On Rank-Based considerations for Generalized Linear Models and Generalized Estimating Equations Models

Committee:
Dr. Joseph W. McKean, Chair
Dr. Michael Stoline
Dr. Jerry Sievers
Dr. Thomas Vidmar
Dr. Joshua Naranjo

Date: Tuesday, October 29, 2002 3:00 p.m. - 5:00 p.m., Grant Room, Rood Hall

Abstract:
This study discusses rank-based robust methods for estimation of parameters and hypotheses testing in the generalized linear models (GLM) and generalized estimating equations (GEE) setting. These models are generalizations of linear and nonlinear models. They allow for both nonlinear mean functions and heteroscedasticity of their random errors. This makes them quite useful in practice.
Rank-based inference has been developed for linear models over the last thirty years. This inference is both robust and highly efficient, and it can be extended to nonlinear models. In this work, we extend this inference to GLM and GEE models.
The robust estimates of the mean function are obtained by minimizing a norm based on Wilcoxon scores in much the same way that least squares type estimates are obtained by minimizing the Euclidean norm. For the heteroscedasticity problem where the errors are independent but have nonconstant variance, we show that these robust estimates retain their consistency and asymptotic normality provided that scale is consistently estimated. We further develop asymptotic theory for robust testing based on both Wald type tests and drop in dispersion tests. In addition, diagnostic tools for outliers and influential observations are developed. We discuss
(over)
extensions to high breakdown estimates. We discuss a robust estimate of the variance- covariance matrix for the auto-regressive structure, used for the GEE models.
Examples and simulation studies illustrate the robustness of the procedure and its superiority against the classical statistical techniques currently used. Data for the examples include a multiple sclerosis longitudinal trial, cholesterol data from randomly selected individuals trial, cholesterol data from randomly selected individuals from the Framingham study, and a nonlinear model based on pharmacokinetic data.

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