Smoothed L-Estimation of Regression Function
CentER Discussion Paper No. 2006-20
23 Pages Posted: 17 Apr 2006
Date Written: March 2006
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
Suggested Citation: Suggested Citation
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