On the Optimality of Multivariate S-Estimators

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 surprising result that in dimensions larger than one, the efficiency of a maxi- mum breakdown S-estimator of location and scatter can get arbitrarily close to 100%, by an appropriate selection of the loss function.Breakdown point;Multivariate Location and Scatter;Robustness;S-estimator

The K-Step Spatial Sign Covariance Matrix

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.

On the optimality of multivariate S-estimators

In this article, 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 per cent for Gaussian errors. We prove the surprising result that in dimensions larger than one, the efficiency of a maximum breakdown S-estimator of location and scatter can get arbitrarily close to 100 per cent, by an appropriate selection of the loss function. © 2010 Board of the Foundation of the Scandinavian Journal of Statistics.status: publishe

On the Optimality of Multivariate S-Estimators

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 surprising result that in dimensions larger than one, the efficiency of a maxi- mum breakdown S-estimator of location and scatter can get arbitrarily close to 100%, by an appropriate selection of the loss function

The K-Step Spatial Sign Covariance Matrix

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

Síndrome de Hughes-Stovin

A síndrome de Hughes-Stovin é uma condição rara, de causa desconhecida, caracterizada pela associação de múltiplos aneurismas de artéria pulmonar e trombose venosa profunda. Alguns autores consideram tal entidade como uma forma incompleta de apresentação da doença de Behçet, devido à semelhança entre os achados radiológicos e anatomopatológicos do comprometimento pulmonar. Os autores relatam um caso de síndrome de Hughes-Stovin cujo primeiro evento trombótico venoso antecedeu em cinco anos o aparecimento dos aneurismas pulmonares