Smoothed L-Estimation of Regression Function

Abstract

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data. This sensitivity can be reduced, for example, by using local L-estimates of regression. Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function. The asymptotic distribution of the proposed estimator is derived under mild B-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical finite-sample improvements. Finally, the proposed method is applied to the modelling of implied volatility.

Keywords: nonparametric regression, L-estimation, smoothed cumulative distribution function

JEL Classification: C13, C14