good predictive behavior. Before showing some of the properties of the MM-estimate, we set the notation for norms of vectors and matrices that we will use later: Given v ∈ R $^{m}$, we denote its 2-norm or Euclidean norm as: where v$_{i}$ represents the i th element of v . Given a matrix A ∈ R r × $^{m}$, its spectral norm ‖ · ‖ $_{sp}$, is defined as follows: Its 2-norm or Frobenius norm ‖ · ‖ 2 is its Euclidean norm if we think the matrix A as a vector of R $^{m.r}$, i.e. where a$_{ij}$ represents to the ( i, j )th element of the matrix A and tr( · ) denotes the trace. Given V ∈ R m × m we denote its eigenvalues as 28 λ$_{1}$ ( V ) ≥ . . . ≥ λ$_{m}$ ( V ) , ‖ A ‖ 2 = [tr( A $^{′}$A )] 1 / 2 = ( m ∑ i =1 n ∑ j =1 | a$_{ij}$ | 2 ) 1 / 2 , (A.2) ‖ A ‖ = ‖ A ‖ sp = max {‖ Av ‖ : v ∈ R m with ‖ v ‖ = 1 } = max { ‖ Av ‖ v : v ∈ R m with v = 0 . (A.1) ‖ v ‖ = ‖ v ‖ 2 = ( m ∑ i =1 v 2 i ) 1 / 2 , A Appendix