Smoothed influence function : another view at robust nonparametric regression

In this work, we introduce a smoothed influence function that constitute a theoretical tool for studying the outliers robustness properties of a large class of nonparametric estimators. With this tool, we first show the nonrobustness of the Nadaraya-Watson estimator of regression. Then we show that the M, the L and the R-estimators of the regression achieve robustness (when estimated by kernel). Our results are illustrated performing Monte-Carlo simulation. -- robustness ; nonparametric regression ; influence function ; M-estimator ; L-estimator ; R-estimator ; Von-mises statistical functional generalized Delta-theorem