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The K-Step Spatial Sign Covariance Matrix

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  • Croux, C.
  • Dehon, C.
  • Yadine, A.

    (Tilburg University, Center for Economic Research)

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.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2010-41.

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Date of creation: 2010
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Handle: RePEc:dgr:kubcen:201041

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  1. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
  2. Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.
  3. Rousseeuw, Peter J. & Croux, Christophe, 1994. "The bias of k-step M-estimators," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 411-420, August.
  4. 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.
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