Weighted Kernel regression

Abstract

In the fixed design regression model, additional weights are considered for the Nadaraya--Watson and Gasser--M\"uller kernel estimators. We study their asymptotic behavior and the relationships between new and classical estimators. For a simple family of weights, and considering the IMSE as global loss criterion, we show some possible theoretical advantages. An empirical study illustrates the performance of the weighted estimators in finite samples.