Weighted Semiparametric Estimation in Regression Analysis with Missing Covariate Data

This article investigates estimation of the regression coefficients in an assumed mean function when covariates on some subjects are missing. We examine the performance of a Horvitz and Thompson (1952)-type weighted estimator by using different estimates of the selection probabilities, which may be treated as nuisance parameters (or a nuisance function). In particular, we investigate the properties of the estimate of the regression parameters when the selection probabilities are estimated by kernel smoothers. We present large sample theory for the new estimator and conduct simulation studies comparing the proposed estimator to the maximum likelihood estimator and multiple imputation under various model assumptions and different missingness mechanisms. In addition, we provide two real examples that motivate this investigation.