Robust Nonparametric Function Estimation for Errors-in-variables Models

This paper discusses robust nonparametric estimators of location regression function for errors-in-variables model with de-convolution kernel. The local constant smoother is used for the estimation of the nonparametric function, and the local linear smoother is proposed to deal with the boundary problem, as well as to improve the local constant smoother. We establish the asymptotic properties of the estimator, the in uence function of the statistical functional and the breakdown point. A simulation study is carried out to demonstrate robust performance of the proposed estimator. The motorcycle data is presented to illustrate the application of the robust estimator further.