Asymptotic Theory for Relative-Risk Models with Missing Time-Dependent Covariates

作     者：Zai-ying ZHOU Peng-cheng ZHANG Ying YANG 

作者机构：Department of Mathematical Sciences Tsinghua University Beijing 100084 China Center for Statistical Science of Tsinghua University Beijing 100084 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2018年第34卷第4期

页      面：669-692页

核心收录：

学科分类：12[管理学] 02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：funded by National Natural Science Foundation of China(NSFC No.11771241) Natural Science Foundation of Anhui Province(No.1708085QA14) 

主　　题：relative-risk model missing time-dependent covariate nonparametric maximum likelihood esti-mation asymptotic normality 

摘      要：Relative-risk models are often used to characterize the relationship between survival time and time-dependent covariates. When the covariates are observed, the estimation and asymptotic theory for parameters of interest are available; challenges remain when missingness occurs. A popular approach at hand is to jointly model survival data and longitudinal data. This seems efficient, in making use of more information, but the rigorous theoretical studies have long been ignored. For both additive risk models and relative-risk models, we consider the missing data nonignorable. Under general regularity conditions, we prove asymptotic normality for the nonparametric maximum likelihood estimators.