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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.

MSC:

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

Software:

robustbase
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References:

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