Proof of Proposition 7: Consider first the case Σ$_{0}$ = I$_{q}$ . The matrix Λ defined in (6.2) can also be expressed as Since W$_{1}$ is differentiable with bounded derivative we can differentiating inside the expectation. We can now proceed analogously to the proof of (A.28) and we have that Using the same arguments as before and W ( u ) = ψ$_{1}$ ( u ) /u , we obtain Since ( E$_{G}$$_{0}$ xx ′ ⊗ I$_{q}$ ) − 1 = ( E$_{G}$$_{0}$ xx $^{′}$)− 1 ⊗ I$_{q}$ , the Proposition is proved for the case Σ$_{0}$ = I$_{q}$ . For the general case, let R a matrix such that Σ$_{0}$ = RR and consider the following transformation y ∗ = R − $^{1}$y . Then B ∗ 0 = B$_{0}$R ′− 1 and y ∗ = B ∗ 0 $^{′}$x + u $^{∗}$, with u ∗ = R − $^{1}$u . Observe that the distribution of u ∗ is given by the density (4.1) with Σ$_{0}$ = I$_{q}$ and and therefore, by the affine-equivariance of the MM-estimates, (6.4) follows. ■ 58 vec( B ′ $_{0}$) = vec( RB ∗ 0 $^{′}$) = ( I$_{p}$ ⊗ R )vec( B ∗ 0 $^{′}$) , M = ( E$_{F}$$_{0}$ [ W ( ‖ u ‖ σ$_{0}$ )] 2 ‖ u ‖ 2 q ) E$_{G}$$_{0}$ xx ′ ⊗ I$_{q}$ = E$_{F}$$_{0}$ ψ$_{1}$ ‖ u ‖ σ$_{0}$ 2 σ 2 0 q ) E$_{G}$$_{0}$ xx ′ ⊗ I$_{q}$ . Λ = − [ E$_{F}$$_{0}$W ′ $_{1}$( ‖ u ‖ $^{2}$/σ2 $_{0}$) ‖ u ‖ 2 qσ 2 0 + E$_{F}$$_{0}$W ( ‖ u ‖ σ$_{0}$ )] ( E$_{G}$$_{0}$ xx ′ ⊗ I$_{q}$ ) . Λ = ∂E$_{H}$$_{0}$W$_{1}$ ( d ( B , Σ ) $^{2}$) vec(( y − B $^{′}$x ) x $^{′}$) ∂ vec( B $^{′}$)′ ( B$_{0}$ , σ 2 $_{0}$I$_{q}$ ) .