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Robust estimation of dimension reduction space

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  • Pavel Cizek
  • Wolfgang Härdle

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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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-015.

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Length: 18 pages
Date of creation: Mar 2005
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2005-015

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Keywords: Dimension reduction; Nonparametric regression; M-estimation;

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References

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  1. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
  2. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 529-568, May.
  3. 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.
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Cited by:
  1. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(1), pages 130-142, January.
  2. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 104(1), pages 88-100, February.
  3. Cizek, P. & Tamine, J. & Härdle, W.K., 2006. "Smoothed L-estimation of Regression Function," Discussion Paper, Tilburg University, Center for Economic Research 2006-20, Tilburg University, Center for Economic Research.
  4. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 63(C), pages 42-49.

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