Oracle-efficient estimation for the mean function of missing covariate data based on noparametrically estimated selection probabilities

Abstract

A weighted local linear estimator for the mean function is constructed based on nonparametrically estimated selection probabilities when covariates are missing at random. The weighted estimator is shown to be oracle-efficient, meaning it is uniformly as efficient as the infeasible estimator that uses the true selection probabilities assumed to be known as a prior. By applying oracle efficiency and the extreme value distribution of the weighted local linear estimator, asymptotically accurate simultaneous confidence bands for the mean function are derived. This approach avoids the risk of model misspecification for the missingness mechanism. Simulation studies are conducted to examine the finite sample performance, which supports the asymptotic results. The proposed methods are illustrated through the analysis of two real data sets.