Smoothed L-Estimation of Regression Function

CentER Discussion Paper No. 2006-20

23 Pages Posted: 17 Apr 2006

See all articles by Pavel Cizek

Pavel Cizek

Tilburg University - Department of Econometrics & Operations Research

Julien Tamine

University of Angers - Research Group in Quantitative Saving (GREQAM)

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin; Charles University; National Yang Ming Chiao Tung University; Asian Competitiveness Institute

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

Cizek, Pavel and Tamine, Julien and Härdle, Wolfgang Karl, Smoothed L-Estimation of Regression Function (March 2006). CentER Discussion Paper No. 2006-20, Available at SSRN: https://ssrn.com/abstract=895468 or http://dx.doi.org/10.2139/ssrn.895468

Pavel Cizek (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Julien Tamine

University of Angers - Research Group in Quantitative Saving (GREQAM) ( email )

Centre de la Vieille Charité
2, rue de la Charité
Marseille, 13002
France

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Asian Competitiveness Institute ( email )

Singapore