Weighted nonparametric regression

Abstract

In the fixed design regression model, additional weights are considered for the Nadaraya-Watson and Gasser-Muller kernel estimators. We study their asymptotic behavior and the relationships between new and classical estimators. For a simple family of weights, and considering the AIMSE as global loss criterion, we show some possible theoretical advantages. An empirical study illustrates the performance of the weighted kernel estimators in theoretical ideal situations and in simulated data sets. Also some results concerning the use of weights for local polynomial estimators are given.