Type of Document Master's Thesis Author Jinnah, Ali Author's Email Address ajinnah1@student.gsu.edu URN etd-11272007-223933 Title INFERENCE FOR COX’S REGRESSION MODEL VIA A NEW VERSION OF EMPIRICAL LIKELIHOOD Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Yichuan Zhao Committee Chair Dr. Xu Zhang Committee Member Dr. Yu-Sheng Hsu Committee Member Dr. Yuanhui Xiao Committee Member Keywords
- coverage probability
- Adjusted Empirical Likelihood
- Normal Approximation
- Empirical Likelihood
- confidence range
- Cox’s regression model
Date of Defense 2007-08-03 Availability unrestricted 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.Files
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