On the Optimality of Multivariate S-Estimators

C. Croux, C. Dehon, A. Yadine

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    Abstract

    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
    PublisherEconometrics
    Number of pages17
    Volume2010-39
    Publication statusPublished - 2010

    Publication series

    NameCentER Discussion Paper
    Volume2010-39

    Keywords

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

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    Croux, C., Dehon, C., & Yadine, A. (2010). On the Optimality of Multivariate S-Estimators. (CentER Discussion Paper; Vol. 2010-39). Econometrics.