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.