Article (Scientific journals)
Location adjustment for the minimum volume ellipsoid estimator
Croux, C.; Haesbroeck, Gentiane; Rousseeuw, P. J.
2002In Statistics and Computing, 12 (3), p. 191-200
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Keywords :
intercept adjustment; L-1 estimation; location estimation; location adjustment; minimum volume ellipsoid; robustness
Abstract :
[en] Estimating multivariate location and scatter with both affine equivariance and positive breakdown has always been difficult. A well-known estimator which satisfies both properties is the Minimum Volume Ellipsoid Estimator (MVE). Computing the exact MVE is often not feasible, so one usually resorts to an approximate algorithm. In the regression setup, algorithms for positive-breakdown estimators like Least Median of Squares typically recompute the intercept at each step, to improve the result. This approach is called intercept adjustment. In this paper we show that a similar technique, called location adjustment, can be applied to the MVE. For this purpose we use the Minimum Volume Ball (MVB), in order to lower the MVE objective function. An exact algorithm for calculating the MVB is presented. As an alternative to MVB location adjustment we propose L-1 location adjustment, which does not necessarily lower the MVE objective function but yields more efficient estimates for the location part. Simulations compare the two types of location adjustment. We also obtain the maxbias curves of both L-1 and the MVB in the multivariate setting, revealing the superiority of L-1.
Disciplines :
Mathematics
Computer science
Author, co-author :
Croux, C.
Haesbroeck, Gentiane ;  Université de Liège - ULiège > Département de mathématique > Statistique (aspects théoriques)
Rousseeuw, P. J.
Language :
English
Title :
Location adjustment for the minimum volume ellipsoid estimator
Publication date :
July 2002
Journal title :
Statistics and Computing
ISSN :
0960-3174
eISSN :
1573-1375
Publisher :
Kluwer Academic Publ, Dordrecht, Netherlands
Volume :
12
Issue :
3
Pages :
191-200
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 23 September 2009

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