content_image/307968.jpg content_image/307967.jpg content_image/307966.jpg content_image/307965.jpg content_image/307964.jpg
estimate ( ˜ B$_{n}$ , ˜ Σ$_{n}$ ) and 

Let 

<img src='content_image/307968.jpg'>

<img src='content_image/307967.jpg'>

be respectively an MM-estimate for the MLM and its initial estimate computed with the sample Z ∗ ∈ Z $_{m}$. 

Then by (2.6), (2.4) and (2.1) 

Moreover, since sup ρ$_{1}$ ( u ) = 1, we get 

Then there exists c < ∞ , that does not depend on Z $^{∗}$, such that, for at least [ n/ 2] observations of Z $^{∗}$, d 2 $_{i}$( ̂ B ∗ $_{n}$, ̂ Σ ∗ $_{n}$) < c . Now, since m < [ n/ 2] − k$_{n}$ , at least k$_{n}$ + 1 of these observations are in Z , 

and not in a hyperplane. Then the smallest eigenvalue of ̂ Σ ∗ $_{n}$, λ$_{q}$ ( ̂ Σ ∗ $_{n}$), is bounded below with a positive bound (for every x$_{i}$ ∈ R $^{p}$, the axis of the ellipsoid 

<img src='content_image/307966.jpg'>

<img src='content_image/307965.jpg'>

<img src='content_image/307964.jpg'>

