Smoothed L-estimation of Regression Function

P. Cizek, J. Tamine, W.K. Härdle

Research output: Working paperDiscussion paperOther research output

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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

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Regression Function
Conditional Distribution
Distribution Function
Regression
Nadaraya-Watson Estimator
Implied Volatility
Mixing Conditions
Empirical Distribution
Nonparametric Estimator
Asymptotic distribution
Outlier
Estimator
Modeling
Estimate

Keywords

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

Cite this

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

Smoothed L-estimation of Regression Function. / Cizek, P.; Tamine, J.; Härdle, W.K.

Tilburg : Econometrics, 2006. (CentER Discussion Paper; Vol. 2006-20).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Smoothed L-estimation of Regression Function

AU - Cizek, P.

AU - Tamine, J.

AU - Härdle, W.K.

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PY - 2006

Y1 - 2006

N2 - 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

AB - 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

KW - nonparametric regression

KW - L-estimation

KW - smoothed cumulative distribution function

M3 - Discussion paper

VL - 2006-20

T3 - CentER Discussion Paper

BT - Smoothed L-estimation of Regression Function

PB - Econometrics

CY - Tilburg

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Cizek P, Tamine J, Härdle WK. Smoothed L-estimation of Regression Function. Tilburg: Econometrics. 2006. (CentER Discussion Paper).