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.