Smoothed L-estimation of Regression Function

P. Cizek, J. Tamine, W.K. Härdle

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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 ¯-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical ¯nite-sample improvements.Finally, the proposed method is applied to the modelling of implied volatility
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages24
Volume2006-20
Publication statusPublished - 2006

Publication series

NameCentER Discussion Paper
Volume2006-20

Keywords

  • nonparametric regression
  • L-estimation
  • smoothed cumulative distribution function

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    Cizek, P., Tamine, J., & Härdle, W. K. (2006). Smoothed L-estimation of Regression Function. (CentER Discussion Paper; Vol. 2006-20). Econometrics.