Robust estimation in partially linear errors-in-variables models

Abstract

In many applications of regression analysis, there are covariates that are measured with errors. A robust family of estimators of the parametric and nonparametric components of a structural partially linear errors-in-variables model is introduced. The proposed estimators are based on a three-step procedure where robust orthogonal regression estimators are combined with robust smoothing techniques. Under regularity conditions, it is proved that the resulting estimators are consistent. The robustness of the proposal is studied by means of the empirical influence function when the linear parameter is estimated using the orthogonal M-estimator. A simulation study allows to compare the behaviour of the robust estimators with their classical relatives and a real example data is analysed to illustrate the performance of the proposal.