| Abstract: | Abstract. 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. |
