Estimation and testing for partially functional linear errors-in-variables models

Abstract

This paper considers estimation and testing problems for partial functional linear models when the covariates in the non-functional linear component are measured with additive error. A corrected profile, least-squares based, estimation procedure is developed for the parametric component. Asymptotic properties of the proposed estimators are established under some regularity conditions. To test a hypothesis on the parametric component, a statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses is proposed; its limiting null distribution is shown to be a weighted sum of independent standard χ12 variables. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for illustration.