Local Polynomial Estimation Of Functional-coefficient Partially Linear Error-in-variable Model

Functional-coefficient partially linear regression model has found wildly applica-tions, but there exists some problems in estimation of constant part and coefficient functions because of they have the different variables. Moreover, in practice, the data al-ways has the measurement errors, and the functional-coefficient partially linear regression model with measurement errors(EV model) introduced in paper can provide a wonder-ful estimation based on the data with measurement errors. Hence it has theoretical and practical significance to study EV model.The purpose of this paper is to study the estimations of constant part and coeffi-cient functions of EV model. First, the initial estimations of constant part and coefficient functions are given by using the local linear technique and the averaged method. Sec-ond, based on the initial estimations, the efficient estimations of the constant part and coefficient functions are proposed by using a one-step back-fitting procedure. Last, the estimations in EV model are proposed by using local corrected. and we also proof that the constant part and coefficient functions have asymptotic normality properties. At the last section, we do the simulation to show that the estimations of EV model is desirable.