TY - JOUR

T1 - Semiparametric double robust and efficient estimation for mean functionals with response missing at random

AU - Guo, Xu

AU - Fang, Yun

AU - Zhu, Xuehu

AU - Xu, Wangli

AU - ZHU, Lixing

N1 - Funding Information:
The research described here is partially supported by National Natural Science Foundation of China ( 11601227 , 11671042 , 11601415 , 11471335 ); a GRF grant from the Research Grants Council of Hong Kong ; China Postdoctoral Science Foundation (No. 2016M590934 , No. 2017T100731 ); and the Fundamental Research Funds for the Central Universities . The authors are grateful to the editor, the associate editor and the three anonymous referees for the constructive comments and suggestions that led to significant improvement of an early manuscript.

PY - 2018/12

Y1 - 2018/12

N2 - Under dimension reduction structure, several semiparametric estimators for the mean of missing response are proposed, which can efficiently deal with the dimensionality problem. Specifically, a generalized version of Augmented Inverse Probability Weighting estimator (AIPW) is proposed and its double robustness, estimation consistency and asymptotic efficiency are investigated. A generalized version of Inverse Probability Weighting (IPW) estimator is also introduced. An asymptotic efficiency reduction phenomenon occurs in the sense that the IPW estimator with the true selection probability is asymptotically less efficient than the one with an estimated selection probability. Besides, two partial imputation and two complete imputation estimators are discussed. We further systematically investigate the comparisons among these estimators in theory. Several simulation studies and a real data analysis are conducted for performance examination and illustration.

AB - Under dimension reduction structure, several semiparametric estimators for the mean of missing response are proposed, which can efficiently deal with the dimensionality problem. Specifically, a generalized version of Augmented Inverse Probability Weighting estimator (AIPW) is proposed and its double robustness, estimation consistency and asymptotic efficiency are investigated. A generalized version of Inverse Probability Weighting (IPW) estimator is also introduced. An asymptotic efficiency reduction phenomenon occurs in the sense that the IPW estimator with the true selection probability is asymptotically less efficient than the one with an estimated selection probability. Besides, two partial imputation and two complete imputation estimators are discussed. We further systematically investigate the comparisons among these estimators in theory. Several simulation studies and a real data analysis are conducted for performance examination and illustration.

KW - Dimension reduction

KW - Double robustness

KW - Inverse probability weighting

KW - Missing at random

UR - http://www.scopus.com/inward/record.url?scp=85051627292&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2018.07.017

DO - 10.1016/j.csda.2018.07.017

M3 - Article

AN - SCOPUS:85051627292

SN - 0167-9473

VL - 128

SP - 325

EP - 339

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

ER -