Missing data mechanism often depends on the values of the responses,which leads to nonignorable nonresponses.In such a situation,inference based on approaches that ignore the missing data mechanism could not be valid....Missing data mechanism often depends on the values of the responses,which leads to nonignorable nonresponses.In such a situation,inference based on approaches that ignore the missing data mechanism could not be valid.A crucial step is to model the nature of missingness.We specify a parametric model for missingness mechanism,and then propose a conditional score function approach for estimation.This approach imputes the score function by taking the conditional expectation of the score function for the missing data given the available information.Inference procedure is then followed by replacing unknown terms with the related nonparametric estimators based on the observed data.The proposed score function does not suffer from the non-identifiability problem,and the proposed estimator is shown to be consistent and asymptotically normal.We also construct a confidence region for the parameter of interest using empirical likelihood method.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to a data set from research in a growth hormone and exercise intervention study.展开更多
基金a College Talent Cultivated by "Thousand-Hundred-Ten" Program of Guangdong Province,National Natural Science Foundation of China(Grant Nos.11471086 and 11101442)the China Scholarship Council(Grant No.201408440400)+5 种基金Humans and Social Science Research Team of Guangzhou University(Grant No.201503XSTD)the Training Program for Excellent Young College Teachers of Guangdong Province(Grant No.Yq201404)the State Key Program of National Natural Science Foundation of China(Grant No.71331006)the State Key Program in the Major Research Plan of National Natural Science Foundation of China(Grant No.91546202)National Center for Mathematics and Interdisciplinary Sciences (NCMIS),Key Laboratory of Key Lab of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)Innovative Research Team of Shanghai University of Finance and Economics(Grant No.IRTSHUFE13122402)
文摘Missing data mechanism often depends on the values of the responses,which leads to nonignorable nonresponses.In such a situation,inference based on approaches that ignore the missing data mechanism could not be valid.A crucial step is to model the nature of missingness.We specify a parametric model for missingness mechanism,and then propose a conditional score function approach for estimation.This approach imputes the score function by taking the conditional expectation of the score function for the missing data given the available information.Inference procedure is then followed by replacing unknown terms with the related nonparametric estimators based on the observed data.The proposed score function does not suffer from the non-identifiability problem,and the proposed estimator is shown to be consistent and asymptotically normal.We also construct a confidence region for the parameter of interest using empirical likelihood method.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to a data set from research in a growth hormone and exercise intervention study.
