Cross-checking using the minimum volume ellipsoid estimator

We show that for a wide class of elliptic models the minimum volume ellipsoid estimator is strongly consistent and the estimating functional is continuous with respect to a weak metric. We also propose to compute an efficient estimator cross-checked by the minimum volume ellipsoid estimator. The former is taken if both estimators stay close to each other based on an affine invariant discrepancy measure. Otherwise, a high breakdown point procedure is called for. This allows us to retain good efficiency for uncontaminated data and at the same time protect against gross errors.