with respect to ˜ Σ ( k ) and ˜ Σ ( k − 1) respectively are smaller than a given value δ . The following theorem, whose proof can be found in the Appendix, shows that the iterative procedure to compute MM-estimates yields the descent of the objective function. Theorem 8. If W ( u ) is nonincreasing in | u | then at each iteration of the algo- rithm the function ∑ n i $_{=1}$ρ$_{1}$ ( d$_{i}$ ( B , Σ )) is nonincreasing. To investigate the performance of the proposed estimates we performed a simu- lation study. - We consider the MLM given by (1.1) for two cases: p = 2, q = 2 and p = 2, q = 5. Due to the equivariance of the estimators we take, without loss of gen- erality, B$_{0}$ = 0 and Σ$_{0}$ = I$_{q}$ . The errors u$_{i}$ are generated from an N$_{q}$ ( 0 , I ) distribution and the predictors x$_{i}$ from an N$_{p}$ ( 0 , I ) distribution. - The sample size is 100 and the number of replications is 1000. We consider uncontaminated samples and samples that contain 10% of identical outliers of the form ( x$_{0}$ , y$_{0}$ ) with x$_{0}$ = ( x$_{0}$, 0 , . . . , 0) and y$_{0}$ = ( mx$_{0}$, 0 , . . . , 0). The values of x$_{0}$ considered are 1 (low leverage outliers) and 10 (high leverage outliers). We take a grid of values of m , starting at 0. The grid was chosen in order that all robust estimates attain the maximum values of their error measure. - Let ̂ B ( k ) be the estimate of B$_{0}$ obtained in the k th replication. Then, since we 17 8 Simulation 8.1 Simulation design