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Robust estimation of dimension reduction space

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  • Cizek, P.
  • Hardle, W.

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 su±ciently 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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Suggested Citation

  • Cizek, P. & Hardle, W., 2006. "Robust estimation of dimension reduction space," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 545-555, November.
    • Handle: RePEc:eee:csdana:v:51:y:2006:i:2:p:545-555
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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.
    2. Yao, Qiwei & Tong, Howell, 1994. "On subset selection in non-parametric stochastic regression," LSE Research Online Documents on Economics 6409, London School of Economics and Political Science, LSE Library.
    3. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
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    Cited by:

    1. Ci­zek, P. & Tamine, J. & Härdle, W., 2008. "Smoothed L-estimation of regression function," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5154-5162, August.
    2. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.
    3. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    4. Zhou, Jingke & Xu, Wangli & Zhu, Lixing, 2015. "Robust estimating equation-based sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 99-118.
    5. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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