A note on kernel assisted estimators in missing covariate regression

We investigate the asymptotic relationships among three kernel assisted semiparametric estimators in regression analysis when some covariates are missing or measured with error. Smoothing techniques are employed in estimating the selection probabilities and the conditionally expected scores, a step which is required to obtain the estimators of interest. The asymptotic distributional properties of these estimators are derived and their asymptotic equivalence is shown. Some important differences are also noted. Furthermore, the asymptotic efficiency of the estimators relative to the usual maximum likelihood estimator is obtained.