Smoothed influence function: Another view at robust nonparametric regression - Julien Tamine (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2001)
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.
urn:nbn:de:kobv:11-10049243
Keywords: C13; C14; C15; 330; robustness; nonparametric regression; influence function; M-estimator; L-estimator; R-estimator; Von-mises statistical functional generalized Delta-theorem