and by (2.4) and (2.1) and this proves the Theorem. ■ Before proving Theorem 2 we will give some results on matrix derivatives that will be used later. Let b be a vector and V be a symmetric matrix, if V is nonsingular, and For further details see Chapter 17 of [24]. Let ( B , Σ ) ∈ R p × q × S $_{q}$, using vec( B $^{′}$A ) = ( A ⊗ I$_{q}$ )vec( B $^{′}$), it is easy to check that From (A.16) and (A.13) it follows that Proof of Theorem 2: The definition of MM-estimates can be reformulated, us- ing the function Γ ( Σ ) := Σ / | Σ | 1 $^{/q}$, in the following way: let ( ̂ B$_{n}$ , C$_{n}$ ) be any 33 n ∑ i =1 ρ$_{1}$ ( d$_{i}$ ( ˜ B$_{n}$ , ˜ Γ$_{n}$ ) ˆ σ$_{n}$ ) ≤ n ∑ i =1 ρ$_{0}$ ( d$_{i}$ ( ˜ B$_{n}$ , ˜ Γ$_{n}$ ) ˆ σ$_{n}$ ) = n 2 , ∂ b $^{′}$Vb ∂ b ′ = 2 b $^{′}$V , (A.13) ∂ | V | ∂ V = | V | V − 1 (A.14) ∂ b $^{′}$V− $^{1}$b ∂ V = − V − $^{1}$bb $^{′}$V− $^{1}$. (A.15) ∂ vec( B $^{′}$A ) ∂ vec( B $^{′}$)′ = ( A ′ ⊗ I$_{q}$ ) . (A.16) ∂d ( B , Σ ) ∂ vec( B $^{′}$)′ = − ( y − B $^{′}$x ) $^{′}$Σ− $^{1}$( x ′ ⊗ I$_{q}$ ) d ( B , Σ ) . (A.17)