Author

Xue YuFollow

Date of Award

7-28-2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

First Advisor

Yichuan Zhao

Second Advisor

Xin Qi

Third Advisor

Jing Zhang

Fourth Advisor

Yichen Cheng

Abstract

In survival analysis, different regression models are used to estimate the effects of covariates on the survival time. The proportional hazards model is commonly applied. However, the proportional hazards model does not always give good fit in the real life. Other models, such as proportional odds models, additive hazards models are useful alternative. Motivated by this limitation, we investigate empirical likelihood method and make inference for semiparametric transformation models and accelerated failure time models in this dissertation. The proposed empirical likelihood methods can solve several challenging and open problems. These interesting problems include semiparametirc transformation model with length-biased sampling, semiparametric analysis based on weighted estimating equations with missing covariates. In addition, a more computationally efficient method called jackknife empirical likelihood (JEL) is proposed, which can be applied to make statistical inference for the accelerated failure time model without computing the limiting variance. We show that under certain regularity conditions, the empirical log-likelihood ratio test statistic converges to a standard chi-squared distribution. Finally, computational algorithms are developed for utilizing the proposed empirical likelihood and jackknife empirical likelihood methods. Extensive simulation studies on coverage probabilities and average lengths of confidence intervals for the regression parameters for those topics indicate good finite samples performance under various settings. Furthermore, for each model, real data sets are analyzed for illustration of the proposed methods.

DOI

https://doi.org/10.57709/12486489

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