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The k-step spatial sign covariance matrix

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  • C. Croux

    ()

  • C. Dehon

    ()

  • A. Yadine

    ()

Abstract

The Sign Covariance Matrix is an orthogonal equivariant estimator of mul- tivariate scale. It is often used as an easy-to-compute and highly robust estimator. In this paper we propose a k-step version of the Sign Covariance Matrix, which improves its e±ciency while keeping the maximal breakdown point. If k tends to infinity, Tyler's M-estimator is obtained. It turns out that even for very low values of k, one gets almost the same e±ciency as Tyler's M-estimator.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s11634-010-0062-7
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Bibliographic Info

Article provided by Springer in its journal Advances in Data Analysis and Classification.

Volume (Year): 4 (2010)
Issue (Month): 2 (September)
Pages: 137-150

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Handle: RePEc:spr:advdac:v:4:y:2010:i:2:p:137-150

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Web page: http://www.springer.com/statistics/statistical+theory+and+methods/journal/11634

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Related research

Keywords: Breakdown point; Multivariate analysis; Principal components; Robust estimation; Spatial signs; 62;

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  1. Rousseeuw, Peter J. & Croux, Christophe, 1994. "The bias of k-step M-estimators," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 411-420, August.
  2. Lutz Dümbgen & David E. Tyler, 2005. "On the Breakdown Properties of Some Multivariate M-Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 247-264.
  3. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
  4. Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.
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