The asymptotics of Rousseeuw's minimum volume ellipsoid estimator

P.L. Davies

doi:10.1214/aos/1176348891

The asymptotics of Rousseeuw's minimum volume ellipsoid estimator

P.L. Davies

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Abstract

Rousseeuw's minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator. In this paper we establish that it satisfies a local Holder condition of order $1/2$ and converges weakly at the rate of $n^{-1/3}$ to a non-Gaussian distribution.

Original language	English
Pages (from-to)	1828-1843
Journal	The Annals of Statistics
Volume	20
Issue number	4
DOIs	https://doi.org/10.1214/aos/1176348891
Publication status	Published - 1992

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title = "The asymptotics of Rousseeuw's minimum volume ellipsoid estimator",

abstract = "Rousseeuw's minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator. In this paper we establish that it satisfies a local Holder condition of order $1/2$ and converges weakly at the rate of $n^{-1/3}$ to a non-Gaussian distribution.",

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AB - Rousseeuw's minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator. In this paper we establish that it satisfies a local Holder condition of order $1/2$ and converges weakly at the rate of $n^{-1/3}$ to a non-Gaussian distribution.

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DO - 10.1214/aos/1176348891

M3 - Article

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SP - 1828

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JO - The Annals of Statistics

JF - The Annals of Statistics

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The asymptotics of Rousseeuw's minimum volume ellipsoid estimator

Abstract

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