k-step spatial sign covariance matrix

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.