Robust Estimation of Dimension Reduction Space

P. Cizek, W.K. Härdle

Research output: Working paperDiscussion paperOther research output

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Abstract

Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions.We show that the recently proposed methods by Xia et al.(2002) can be made robust in such a way that preserves all advantages of the original approach.Their extension based on the local one-step M-estimators is sufficiently robust to outliers and data from heavy tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages26
Volume2005-31
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper
Volume2005-31

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outlier
smoothing
method
distribution
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Keywords

  • Dimension reduction
  • Nonparametric regression
  • M-estimation

Cite this

Cizek, P., & Härdle, W. K. (2005). Robust Estimation of Dimension Reduction Space. (CentER Discussion Paper; Vol. 2005-31). Tilburg: Econometrics.
Cizek, P. ; Härdle, W.K. / Robust Estimation of Dimension Reduction Space. Tilburg : Econometrics, 2005. (CentER Discussion Paper).
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Cizek, P & Härdle, WK 2005 'Robust Estimation of Dimension Reduction Space' CentER Discussion Paper, vol. 2005-31, Econometrics, Tilburg.

Robust Estimation of Dimension Reduction Space. / Cizek, P.; Härdle, W.K.

Tilburg : Econometrics, 2005. (CentER Discussion Paper; Vol. 2005-31).

Research output: Working paperDiscussion paperOther research output

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T1 - Robust Estimation of Dimension Reduction Space

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AU - Härdle, W.K.

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N2 - Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions.We show that the recently proposed methods by Xia et al.(2002) can be made robust in such a way that preserves all advantages of the original approach.Their extension based on the local one-step M-estimators is sufficiently robust to outliers and data from heavy tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data.

AB - Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions.We show that the recently proposed methods by Xia et al.(2002) can be made robust in such a way that preserves all advantages of the original approach.Their extension based on the local one-step M-estimators is sufficiently robust to outliers and data from heavy tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data.

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KW - Nonparametric regression

KW - M-estimation

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BT - Robust Estimation of Dimension Reduction Space

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Cizek P, Härdle WK. Robust Estimation of Dimension Reduction Space. Tilburg: Econometrics. 2005. (CentER Discussion Paper).