Estimation in partially linear varying-coefficient errors-in-variables models with missing response variables

In this paper, a partially linear varying-coefficient model with measurement errors in the nonparametric component as well as missing response variable is studied. Two estimators for the parameter vector and nonparametric function are proposed based on the locally corrected profile least squares method. The first estimator is constructed by using the complete-case data only, and another by using an imputation technique. Both proposed estimators of the parametric component are shown to be asymptotically normal, and the estimators of nonparametric function are proved to achieve the optimal strong convergence rate as the usual nonparametric regression. Some simulation studies are conducted to compare the behavior of these estimators and the results confirm that the estimators based on the imputation technique perform better than the complete-case data estimator in finite samples. Finally, an application to a real data set is illustrated.