Local polynomial regression smoothers with AR-error structure

Abstract

Consider the fixed regression model with random observation error that follows an AR(1) correlation structure. In this paper, we study the nonparametric estimation of the regression function and its derivatives using a modified version of estimators obtained by weighted local polynomial fitting. The asymptotic properties of the proposed estimators are studied; expressions for the bias and the variance/covariance matrix of the estimators are obtained and the joint asymptotic normality is established. In a simulation study, a better behavior of the Mean Integrated Squared Error of the proposed regression estimator with respect to that of the classical local polynomial estimator is observed when the correlation of the observations is large.