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Bounded influence regression using high breakdown scatter matrices

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  • Christophe Croux
  • Stefan Aelst

    ()

  • Catherine Dehon

Abstract

In this paper we estimate the parameters of a regression model using S-estimators of multivariate location and scatter. The approach is proven to be Fisher-consistent, and the influence functions are derived. The corresponding asymptotic variances are obtained and it is shown how they can be estimated in practice. A comparison with other recently proposed robust regression estimators is made.

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File URL: http://hdl.handle.net/10.1007/BF02530499
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Bibliographic Info

Article provided by Springer in its journal Annals of the Institute of Statistical Mathematics.

Volume (Year): 55 (2003)
Issue (Month): 2 (June)
Pages: 265-285

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Handle: RePEc:spr:aistmt:v:55:y:2003:i:2:p:265-285

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Related research

Keywords: Fisher-consistency; influence function; robust regression; S-estimators; scatter matrices;

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References

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  1. Croux, Christophe & Haesbroeck, G, 1999. "Influence function and efficiency of the minimum covariance determinant scatter matrix estimator," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/97158, Katholieke Universiteit Leuven.
  2. Croux, Christophe & Rousseeuw, Peter & Hössjer, O., 1994. "Generalized S-estimators," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/205831, Katholieke Universiteit Leuven.
  3. Croux, Christophe & Dehon, Catherine & Rousseeuw, Peter J. & Aelst, Stefan Van, 2001. "Robust estimation of the conditional median function at elliptical models," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 361-368, February.
  4. Croux, Christophe & Haesbroeck, G, 2000. "Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/99557, Katholieke Universiteit Leuven.
  5. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
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Citations

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Cited by:
  1. Catherine Dehon & Marjorie Gassner & Vincenzo Verardi, 2005. "Robustness or Efficiency, A Test to Solve the Dilemma," Econometrics 0508011, EconWPA.
  2. Croux, Christophe & Dhaene, Geert & Hoorelbeke, Dirk, 2003. "Robust standard errors for robust estimators," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/118271, Katholieke Universiteit Leuven.
  3. Christmann, Andreas & Steinwart, Ingo & Hubert, Mia, 2007. "Robust learning from bites for data mining," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 347-361, September.
  4. Dehon, Catherine & Gassner, Marjorie & Verardi, Vincenzo, 2009. "A Hausman-type test to detect the presence of influential outliers in regression analysis," Economics Letters, Elsevier, vol. 105(1), pages 64-67, October.
  5. Christmann, Andreas & Steinwart, Ingo & Hubert, Mia, 2006. "Robust Learning from Bites for Data Mining," Technical Reports 2006,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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