On the Optimality of Multivariate S-Estimators
AbstractIn 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2010-39.
Date of creation: 2010
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Web page: http://center.uvt.nl
Breakdown point; Multivariate Location and Scatter; Robustness; S-estimator;
Other versions of this item:
- Christophe Croux & Catherine Dehon & Abdelilah Yadine, 2011. "On the Optimality of Multivariate S‐Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 38(2), pages 332-341, 06.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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