Limit Theory Of The MLE For The Proportional Hazards Model With Incomplete Information

We address some important topics in the large-sample theory for the proportional hazards model based on the data with random censorship and incomplete information. In survival analysis the proportional hazards model is a significant regression model and right censoring data with incomplete information is a common data type. The research on proportional hazards model randomly censored with incomplete information is very meaningful. Under suitable assumptions, we obtain the consistency, asymptotic normal-ity, law of iterated logarithm and the moderate deviation of the maximum likelihood estimator of unknown parameters. Most of the conclusions are the first time to be ob-tained.This thesis consists of five parts as follows:In chapter one, We first provide a brief description of the background, previous work, the main results of our work. Then, we introduce the proportional hazards model randomly censored with incomplete information and give the likelihood function.In the second chapter, we obtain the existence, consistency and asymptotic nor-mality of the maximum likelihood estimator under the hypothesis that covariates are non-random.In the third chapter, we prove that the maximum likelihood estimator which ob-tained in the chapter two satisfy the law of iterated logarithm, Chung type law of iterated logarithm and the moderate deviation.In chapter four, under the presumption that covariates are random, the results of the existence, consistency and asymptotic normality, the law of iterated logarithm deviation and the moderate deviation of the maximum likelihood estimator are obtained one by one.In the final chapter, we discuss how to map the quantitative trait loci based on the data randomly censored with incomplete information and propose a corresponding interval mapping method which verified by numerical simulation method.