Premium
On the Optimality of Multivariate S‐Estimators
Author(s) -
CROUX CHRISTOPHE,
DEHON CATHERINE,
YADINE ABDELILAH
Publication year - 2011
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2010.00710.x
Subject(s) - mathematics , estimator , multivariate statistics , bounded function , statistics , constraint (computer aided design) , multivariate normal distribution , minimum variance unbiased estimator , econometrics , mathematical analysis , geometry
. In this article, 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.