MVE, MCD, and MZE: A simulation study comparing convex body minimizers

Summary: In a recent work (Paris Scholz, 2002), a new robust estimator for convex bodies has been proposed, based on the estimation of a zonoid of a distribution. This so–called minimum volume zonoid estimator (MZE) is similar in type to the well–known robust approaches of the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD), all three seeking for a subset of given data for which some criteria are minimized. We investigate the similarity between these three concepts by comparing which subsets are chosen to be the optimal ones.