Estimation of the mean of the partially linear single-index errors-in-variables model with missing response variables

Abstract

In this paper, we estimate the mean of the partially linear single-index errors-in-variables model with missing response variables. The linear covariate is measured with additive error, therefore missing is not random. Two special estimators are defined that include a semiparametric regression imputation estimator and a marginal average estimator. These estimators are shown to be asymptotically normal and have the same asymptotic variance. A simulation experiment is used to illustrate our proposed method.