Location adjustment for the minimum volume ellipsoid estimator View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2002-07

AUTHORS

Christophe Croux, Gentiane Haesbroeck, Peter J. Rousseeuw

ABSTRACT

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 L1location 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 L1 and the MVB in the multivariate setting, revealing the superiority of L1. More... »

PAGES

191-200

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1020713207683

DOI

http://dx.doi.org/10.1023/a:1020713207683

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046591710


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