Estimation and Inference in Semi-Functional Partially Linear Measurement Error Models

This article studies the estimation and statistical inference problems of semi-functional partially linear regression models when the covariates in the linear part are measured with additive error. To obtain the estimation of the parametric component, a corrected profile least-squares based estimation procedure is developed. Asymptotic properties of the proposed estimators are established under some mild assumptions. To test hypothesis on the parametric part, the authors propose a novel test statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses, and show that its limiting distribution is a weighted sum of independent standard χ12. Finally, the authors illustrate the finite sample performance of the methods with some simulation studies and a real data application.