The k-step spatial sign covariance matrix
AbstractThe 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 eÂ±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 eÂ±ciency as Tyler's M-estimator.
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Bibliographic InfoArticle provided by Springer in its journal Advances in Data Analysis and Classification.
Volume (Year): 4 (2010)
Issue (Month): 2 (September)
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Web page: http://www.springer.com/statistics/statistical+theory+and+methods/journal/11634
Other versions of this item:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.
- 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.
- Rousseeuw, Peter J. & Croux, Christophe, 1994. "The bias of k-step M-estimators," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 411-420, August.
- Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
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