On the Optimality of Multivariate S-Estimators

C. Croux, C. Dehon, A. Yadine

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    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.
    Original languageEnglish
    Place of PublicationTilburg
    Number of pages17
    Publication statusPublished - 2010

    Publication series

    NameCentER Discussion Paper


    • Breakdown point
    • Multivariate Location and Scatter
    • Robustness
    • S-estimator


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