Computation of the Minimum Covariance Determinant Estimator

Robust estimation of location and scale in the presence of outliers is an important task in classification. Outlier sensitive estimation will lead to a large number of misclassifications. Rousseeuw introduced two estimators with high breakdown point, namely the minimum-volume-ellipsoid estimator (MVE) and the minimum-covariance-determinant estimator (MCD). While the MCD estimator has better theoretical properties than the MVE, the latter one appears to be used more widely. This may be due to the lack of fast algorithms for computing the MCD, up to now.In this paper two branch-and-bound algorithms for the exact computation of the MCD are presented. The results of their application to simulated samples are compared with a new heuristic algorithm “multistart iterative trimming” and the steepest descent method suggested by Hawkins. The results show that multistart iterative trimming is a good and very fast heuristic for the MCD which can be applied to samples of large size.