A fusion of least squares and empirical likelihood for regression models with a missing binary covariate

作     者：DUAN XiaoGang WANG Zhi 

作者机构：Department of StatisticsBeijing Normal UniversityBeijing 100875China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2016年第59卷第10期

页      面：2027-2036页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 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] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11301031) 

主　　题：calibration covariate adjustment effect modification missing at random multiple robustness refitting 

摘      要：Multiply robust inference has attracted much attention recently in the context of missing response data. An estimation procedure is multiply robust, if it can incorporate information from multiple candidate models, and meanwhile the resulting estimator is consistent as long as one of the candidate models is correctly specified. This property is appealing, since it provides the user a flexible modeling strategy with better protection against model misspecification. We explore this attractive property for the regression models with a binary covariate that is missing at random. We start from a reformulation of the celebrated augmented inverse probability weighted estimating equation, and based on this reformulation, we propose a novel combination of the least squares and empirical likelihood to separately handle each of the two types of multiple candidate models,one for the missing variable regression and the other for the missingness mechanism. Due to the separation, all the working models are fused concisely and effectively. The asymptotic normality of our estimator is established through the theory of estimating function with plugged-in nuisance parameter estimates. The finite-sample performance of our procedure is illustrated both through the simulation studies and the analysis of a dementia data collected by the national Alzheimer s coordinating center.