Approximation algorithms for the estimate of the MCD and a new proposal

In the multidimensional framework the robust estimation of the location and the covariance matrix is a highly expensive computational task. A popular estimator is the Minimum Covariance Determinant (MCD; Rousseeuw, 1984, 1985). Different authors proposed approximation algorithms for this estimator. Recently Rousseeuw and van Driessen (1999) seem to stop the competition in providing a fast and good approximation to the MCD with their procedure called FAST-MCD. This algorithm works fine when the spatial configuration of data contains either radial outliers or clusters of outliers having dispersion higher than that of the good points. When the cluster of outlying observations has a dispersion lower than that of the good points the FAST-MCD shows some drawbacks. This behavior highlights some remarks about the robustness of the MCD. In the talk we review the MCD estimator and some algorithms for its approximation, we discuss about the source of failure of the estimator, and we present a new procedure.