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Robust adaptive estimation of dimension reduction space

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  • Čížek, Pavel
  • Härdle, Wolfgang

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 MAVE and OPG methods by Xia et al. (2002) allow us to make them robust in a relatively straightforward way that preserves all advantages of the original approach. The best of the proposed robust modifications, which we refer to as MAVE-WMAD-R, is sufficiently robust to outliers and data from heavy tailed distributions, it is easy to implement, and surprisingly, it also outperforms the original method in small sample behaviour even when applied to normally distributed data.

Suggested Citation

  • Čížek, Pavel & Härdle, Wolfgang, 2003. "Robust adaptive estimation of dimension reduction space," SFB 373 Discussion Papers 2003,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:20031
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    References listed on IDEAS

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    1. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
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    More about this item

    Keywords

    nonparametric regression; dimension reduction; minimum average variance estimator; robust estimation; median absolute deviation; L1 regression;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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