Dimension-reduced empirical likelihood estimation and inference for M-estimators with nonignorable nonresponse

Abstract

When the responses have nonignorable missing data, we consider a general semiparametric propensity model and propose empirical likelihood (EL) based statistical inference for M-estimators. The unknown parameters in the propensity are firstly identified and estimated by combining instrumental estimating equations and dimension-reduced kernel estimators. We propose three bias-corrected nonparametric estimating equations in conjunction with the EL procedure. The resulting maximum EL estimators are shown asymptotically equivalent, achieve the desirable asymptotic properties of unbiasedness and asymptotic normality. An adjusted EL ratio procedure for constructing accurate confidence regions is also proposed. The finite-sample performance of the proposed estimators for response mean, distribution function and quantile is studied through simulation, and an application to ACTG 175 data set is also presented.

Keywords:

• Dimension reduction
• empirical likelihood
• identifiability
• instrument
• kernel regression
• nonignorable nonresponse

Acknowledgments

The authors are grateful to the Editor, an Associate Editor and two anonymous referees for their insightful comments and suggestions on this article, which have led to significant improvements.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This article was supported by the National Natural Science Foundation of China [grant numbers 11871287, 11771144, 11801359], the Natural Science Foundation of Tianjin [grant numbers 18JCYBJC41100], Fundamental Research Funds for the Central Universities and the Key Laboratory for Medical Data Analysis and Statistical Research of Tianjin, the Laboratory for Economic Behaviors and Policy Simulation, Nankai University. The first two authors contributed equally to this work.