Adaptive empirical likelihood estimation with nonignorable nonresponse data

Abstract

ABSTRACTWe propose adaptive empirical likelihood (EL) estimators to improve estimation efficiency of existing adaptive estimators of the mean response with non-ignorable non-response data. The proposed adaptive EL estimators achieve semiparametric efficiency if the missing probability and conditional distribution of outcome given covariates among the complete cases are both correctly specified. Moreover, if the missing probability is specified correctly, the proposed estimator still achieves a semiparametric efficiency lower bound within a more general class of estimating functions, even if the conditional distribution of outcome is misspecified. The adaptive EL ratio statistic can be used to test whether the missing of the responses is non-ignorable or at random. We also propose kernel-assisted EL estimators of the mean response which achieve semiparametric efficiency if missing probability is correctly specified. The theoretical results are confirmed by a simulation study. A real data example is used to illustrate the proposed adaptive EL method.