Minimum volume ellipsoid

The minimum volume ellipsoid (MVE) estimator is based on the smallest volume ellipsoid that covers h of the n observations. It is an affine equivariant, high-breakdown robust estimator of multivariate location and scatter. The MVE can be computed by a resampling algorithm. Its low bias makes the MVE very useful for outlier detection in multivariate data, often through the use of MVE-based robust distances. We review the basic MVE definition as well as some useful extensions such as the one-step reweighted MVE. We discuss the main properties of the MVE including its breakdown value, affine equivariance, and efficiency. We discuss the basic resampling algorithm to calculate the MVE and illustrate its use on two examples. An overview of applications is given, as well as some related classes of robust estimators of multivariate location and scatter. (C) 2009 John Wiley & Sons, Inc.