  We define the minimum covariance determinant functionals for multivariate
location and scatter through trimming functions and establish their existence
at any multivariate distribution. We provide a precise characterization
including a separating ellipsoid property and prove that the functionals are
continuous. Moreover, we establish asymptotic normality for both the location
and covariance estimator and derive the influence function. These results are
obtained in a very general multivariate setting.
