multivariate regression and the observation i receives the weight W ( d$_{i}$ ( ̂ B$_{n}$ , ̂ Σ$_{n}$ ) ) . Furthermore, by (2.11) , ̂ Σ$_{n}$ is proportional to the sample covariance matrix of the weighted residuals with the same weights. As these weights depend on the estimates ̂ B$_{n}$ and ̂ Σ$_{n}$ , we cannot use the relations (2.10) and (2.11) to compute the estimates, but they will be used to formulate an iterative algorithm in Section 6. Remark 3. If ˜ B$_{n}$ is regression-, affine- and scale-equivariant and ˜ Σ$_{n}$ is affine- equivariant and regression- and scale-invariant. Then ̂ B$_{n}$ will be regression-, affine- and scale-equivariant and ̂ Σ$_{n}$ will be regression- and scale-invariant and affine-equivariant. Now, to investigate the robustness of the MM-estimates, we will seek a lower bound of their finite sample breakdown point. The finite sample breakdown point of the coefficient matrix estimate is the smallest fraction of outliers that make the estimator unbounded, and the finite sample breakdown point of the covari- ance matrix estimate is the smallest fraction of outliers that make the estimate unbounded or singular. Let Z = { z$_{1}$ , . . . , z$_{n}$ } be a sample of size n that satisfies the MLM (1.1), where z$_{i}$ = ( y ′ $_{i}$, x $^{′}$$_{i}$) and let ̂ B and ̂ Σ be estimates of B$_{0}$ and Σ$_{0}$ respectively. We define Z m = { Z ∗ = { z ∗ $_{1}$, . . . , z ∗ n } such that ♯ { i : z$_{i}$ = z ∗ i } ≥ n − m } , S$_{m}$ ( Z , ̂ B ) = sup {‖ ̂ B ( Z $^{∗}$) ‖ 2 with Z ∗ ∈ Z m } , S + $_{m}$( Z , Σ ) = sup { λ$_{1}$ ( ̂ Σ ( Z $^{∗}$)) with Z ∗ ∈ Z m } 8 3 Breakdown Point