Robust corrected empirical likelihood for partially linear measurement error models

This paper considers a partially linear model in which the covariates of parametric part are measured with normal distributed errors. A newly robust corrected empirical likelihood procedure based on the corrected score function is proposed to attenuate the effects of measurement errors as well as outliers. What’s more, profit from the QR decomposition technique, the parametric and nonparametric components of the models can be estimated separately. The asymptotic properties of the proposed robust corrected empirical likelihood approach are established under some regularity conditions. Simulation studies are demonstrated to show that our proposed method performs well in finite samples. Boston housing price data are applied to illustrate the proposed estimation procedure.