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A robust and efficient adaptive reweighted estimator of multivariate location and scatter

✍ Scribed by Daniel Gervini

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 306 KB
Volume: 84
Category: Article
ISSN: 0047-259X
DOI: 10.1016/s0047-259x(02)00018-0

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✦ Synopsis

This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hardrejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200.

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