Publication
Title
Location adjustment for the minimum volume ellipsoid estimator
Author
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 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.
Language
English
Source (journal)
Statistics and computing. - London
Publication
London : 2002
ISSN
0960-3174
Volume/pages
12:3(2002), p. 191-200
ISI
000178716400001
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 03.01.2013
Last edited 13.07.2017
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