Date of Award

11-28-2007

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Dr. Yichuan Zhao - Chair

Second Advisor

Dr. Yu-Sheng Hsu

Third Advisor

Dr. Xu Zhang

Fourth Advisor

Dr. Yuanhui Xiao

Abstract

Cox Proportional Hazard Model is one of the most popular tools used in the study of Survival Analysis. Empirical Likelihood (EL) method has been used to study the Cox Proportional Hazard Model. In recent work by Qin and Jing (2001), empirical likelihood based confidence region is constructed with the assumption that the baseline hazard function is known. However, in Cox’s regression model the baseline hazard function is unspecified. In this thesis, we re-formulate empirical likelihood for the vector of regression parameters by estimating the baseline hazard function. The EL confidence regions are obtained accordingly. In addition, Adjusted Empirical Likelihood (AEL) method is proposed. Furthermore, we conduct extensive simulation studies to evaluate the performance of the proposed empirical likelihood methods in terms of coverage probabilities by comparing with the Normal Approximation based method. The simulation studies show that all the three methods produce similar coverage probabilities.

Included in

Mathematics Commons

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