On the Optimality of Multivariate S-Estimators

C. Croux; C. Dehon; A. Yadine

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 language	English
Place of Publication	Tilburg
Publisher	Econometrics
Number of pages	17
Volume	2010-39
Publication status	Published - 2010

Publication series

Name	CentER Discussion Paper
Volume	2010-39

Keywords

Breakdown point
Multivariate Location and Scatter
Robustness
S-estimator

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2010-39

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title = "On the Optimality of Multivariate S-Estimators",

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.",

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series = "CentER Discussion Paper",

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TY - UNPB

T1 - On the Optimality of Multivariate S-Estimators

AU - Croux, C.

AU - Dehon, C.

AU - Yadine, A.

N1 - Pagination: 17

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Breakdown point

KW - Multivariate Location and Scatter

KW - Robustness

KW - S-estimator

M3 - Discussion paper

VL - 2010-39

T3 - CentER Discussion Paper

BT - On the Optimality of Multivariate S-Estimators

PB - Econometrics

CY - Tilburg

ER -

On the Optimality of Multivariate S-Estimators

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