On the optimality of multivariate S-estimators. (English) Zbl 1246.62136

Summary: 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.


62H12 Estimation in multivariate analysis
62F35 Robustness and adaptive procedures (parametric inference)


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