based on an iterative weighted MLE. In Section 8 we present the results of a simulation study and a real example in Section 9. All the proofs can be found in the Appendix. Before defining our class of robust estimates for the MLM, we will define a robust estimate of scale. Definition 1. Given a sample of size n , v = ( v$_{1}$, . . . , v$_{n}$ ) , an M-estimate of scale s ( v ) is defined as the value of s that is solution of where b ∈ (0 , 1) , or s = 0 if ♯ ( v$_{i}$ = 0) ≥ n (1 − b ) , where ♯ is the symbol for cardinality. In this paper we use b = 0 . 5, which ensures the maximal asymptotic break- down point (see [11]). The function ρ$_{0}$ should satisfy the following definition. Definition 2. A ρ -function will denote a function ρ ( u ) which is a continuous nondecreasing function of | u | such that ρ (0) = 0 , sup$_{u}$ ρ ( u ) = 1 , and ρ ( u ) is increasing for nonnegative u such that ρ ( u ) < 1 . Note that according to the terminology of Maronna et al. [16] this would be a “bounded ρ -function”. A popular ρ -function is the bisquare function : 4 1 n n ∑ i =1 ρ$_{0}$ ( v$_{i}$ s ) = b, (2.1) ρ$_{B}$ ( u ) = 1 − (1 − u $^{2}$)$^{3}$I ( | u | ≤ 1) , (2.2) 2 Definition and properties