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...

Nonparametric correlation estimators as the Kendall and Spearman correlation are widely used in the applied sciences. They are often said to be robust, in the sense of being resistant to outlying observations. In this paper we formally study their robustness by means of their influence functions...

In this note we study the problem of estimating the parameters of the conditional median function at elliptical models. For this we use positive-breakdown estimators of multivariate location and scatter, and obtain influence functions and asymptotic variances of the resulting slope and...

Nonparametric correlation measures at the Kendall and Spearman correlation are widely used in the behavioral sciences. These measures are often said to be robust, in the sense of being resistant to outlying observations. In this note we formally study their robustness by means of their infuence...

In this paper we maximize the efficiency of a multivariate S-estimator under a constraint on the breakdown point. In the linear regression model, it is known that the highest possible efficiency of a maximum breakdown S-estimator is bounded above by 33% for Gaussian errors. We prove the...