The \(k\)-step spatial sign covariance matrix. (English) Zbl 1284.62367

Summary: The sign covariance matrix is an orthogonal equivariant estimator of multivariate 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 efficiency 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 efficiency as Tyler’s M-estimator.


62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H25 Factor analysis and principal components; correspondence analysis
62H12 Estimation in multivariate analysis


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