Robust local polynomial regression for dependent data

Abstract

Let (Xj, Yj)jn=1 be a realization of a bivariate jointly strictly stationary process. We consider a robust estimator of the regression function m(x) = E(Y|X = x) by using local polynomial regression techniques. The estimator is a local M-estimator weighted by a kernel function. Under mixing conditions satisfied by many time series models, together with other appropriate conditions, consistency and asymptotic normality results are established. One-step local M-estimators are introduced to reduce computational burden. In addition, we give a data-driven choice for minimizing the scale factor involving the ψ-function in the asymptotic covariance expression, by drawing a parallel with the class of Huber's ψ-functions. The method is illustrated via two examples.