Consistency is shown for the minimum covariance determinant (MCD) estimators of multivariate location and scale and asymptotic normality is shown for the former. The proofs are made possible by showing a separating ellipsoid property for the MCD subset of observations. An analogous property is shown for the MCD subset computed from the population distribution.
"Asymptotics for the Minimum Covariance Determinant Estimator." Ann. Statist. 21 (3) 1385 - 1400, September, 1993. https://doi.org/10.1214/aos/1176349264