Iterative Likelihood: A Unified Inference Tool

作     者：Wang, Haiying Zhang, Dixin Liang, Hua Ruppert, David 

作者机构：Univ Connecticut Dept Stat Storrs CT 06269 USA Nanjing Univ Dept Finance Nanjing Jiangsu Peoples R China George Washington Univ Dept Stat Washington DC 20052 USA Cornell Univ Dept Stat Sci Ithaca NY USA 

出 版 物：《JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS》 (计算与图解统计学杂志)

年 卷 期：2021年第30卷第4期

页      面：920-933页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：NSF [DMS-1620898] 

主　　题：Asymptotic properties Attraction Censoring EM algorithm Generalized estimating equations Mean score method 

摘      要：We propose a framework for inference based on an iterative likelihood function, which provides a unified representation for a number of iterative approaches, including the EM algorithm and the generalized estimating equations (GEEs). The parameters are decoupled to facilitate construction of the inference vehicle, to simplify computation, or to ensure robustness to model misspecification and then recoupled to retain their original interpretations. For simplicity, throughout the paper, we will refer to the log-likelihood as the likelihood. We define the global, local, and stationary estimates of an iterative likelihood and, correspondingly, the global, local, and stationary attraction points of the expected iterative likelihood. Asymptotic properties of the global, local, and stationary estimates are derived under certain assumptions. An iterative likelihood is usually constructed such that the true value of the parameter is a point of attraction of the expected log-likelihood. Often, one can only verify that the true value of the parameter is a local or stationary attraction, but not a global attraction. We show that when the true value of the parameter is a global attraction, any global estimate is consistent and asymptotically normal;when the true value is a local or stationary attraction, there exists a local or stationary estimate that is consistent and asymptotically normal, with a probability tending to 1. The behavior of the estimates under a misspecified model is also discussed. Our methodology is illustrated with three examples: (i) estimation of the treatment group difference in the level of censored HIV RNA viral load from an AIDS clinical trial;(ii) analysis of the relationship between forced expiratory volume and height in girls from a longitudinal pulmonary function study;and (iii) investigation of the impact of smoking on lung cancer in the presence of DNA adducts. Two additional examples are in the , GEEs with missing covariates and an unweighted