The K-Step Spatial Sign Covariance Matrix

C. Croux; C. Dehon; A. Yadine

The K-Step Spatial Sign Covariance Matrix

C. Croux, C. Dehon, A. Yadine

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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.

Original language	English
Place of Publication	Tilburg
Publisher	Econometrics
Number of pages	13
Volume	2010-41
Publication status	Published - 2010

Publication series

Name	CentER Discussion Paper
Volume	2010-41

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Croux, C., Dehon, C., & Yadine, A. (2010). The K-Step Spatial Sign Covariance Matrix. (CentER Discussion Paper; Vol. 2010-41). Econometrics.

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N2 - 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.

AB - 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.

M3 - Discussion paper

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T3 - CentER Discussion Paper

BT - The K-Step Spatial Sign Covariance Matrix

PB - Econometrics

CY - Tilburg

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2010-41