Smoothed L-estimation of regression function

The Nadaraya-Watson estimator of regression is known to be highly sensitive to the presence of outliers in the sample. A possible way of robusti-fication consists in 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. We show that this smoothed L-estimation approach provides computational as well as statistical finite sample improvements. The asymptotic distribution of the estimator is derived under mild β-mixing conditions.