Robust Mahalanobis distances obtained using the 'multout' and 'fast-mcd' methods

Robust Mahalanobis distances play an essential role in detecting outliers. The robustness is obtained by using for evaluations a robust covariance matrix. We consider two methods of constructing a robust covariance matrix: (i) the 'fast-mcd' (minimum covariance determinant) method proposed by Rousseeuw and van Driessen [14] and (ii) the hybrid method 'multout' proposed by Rocke and Woodruff [12]. The methods are investigated considering six benchmark data sets containing outliers and one medical data set (liver disorders). Both methods yield similar results, though some discrepancies are observed in two of the analyzed benchmark data sets, namely in the 'bushfire' and 'stack-loss' data.