Robust Estimation of Multivariate Location and Scatter based on the Effective Independence Distribution

This paper applies a method known in the engineering literature as Effective Independence Distribution (EID) to an approximation of the minimum volume ellipsoid, a high breakdown robust estimator of multivariate location and scale. The calculation of the minimum volume ellipsoid is an extremely computationally intensive task. Previous methods for approximating the MVE have focused on bootstrap-like resampling techniques. These are neither guaranteed to achieve the minimum volume ellipsoid nor are they necessarily repeatable from investigator to investigator since they use pseudo-random sampling techniques. The method presented here is a hybrid technique which uses the EID methodology to determine the subset selection and then uses well-known techniques to determine the ellipsoid. We also propose an alternate maximum likelihood method for estimating the mean and covariance matrix.