On the optimality of multivariate S-estimators KU Leuven
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 ...