An improvement of the basic resampling scheme for the mcd estimation

In the multidimensional framework the robust estimation of the location and the covariance matrix is an highly expensive computational task. A popular estimator is the Minimum Covariance Determinant (MCD; Rousseeuw, 1984, 1985). Rousseeuw and van Driessen (1999) provided an efficient approximation algorithm for the MCD, called FAST-MCD, and which is able to handle, in a feasible time, large datasets. Some authors (Maronna and Zamar, 2002; Hawkins and Olive, 2002; Juan and Prieto, 2001; Pena and Prieto, 2001) highlighted drawbacks of the FAST-MCD concerning both the consistency and the bias of the estimator and the outlier detection. The present paper proposes a modified version of the FAST-MCD, called CC-MCD, which is able to avoid some sources of failure. The improvement is achieved by picking up an appropriate subset of data where the Elemental sets are randomly drawn from. The approximation to the MCD obtained through the CC-MCD algorithm has nice properties and requires a much smaller number of sampled Elemental sets.