as in (3.1) but with [ n (1 − b )] in place of [ n/ 2]. In this case, the maximum finite sample breakdown point would be attained in b = 0 . 5 − k$_{n}$/n which is very close to our choice of b = 0 . 5 when k$_{n}$/n is small. Consider an estimate ̂ θ$_{n}$ depending on a sample Z = { z$_{1}$ , . . . , z$_{n}$ } of i.i.d. variables in R k with distribution H$_{θ}$ , where θ ∈ Θ ⊂ R $^{m}$. Let T be an estimating functional of θ such that T ( H$_{n}$ ) = ̂ θ$_{n}$ , where H$_{n}$ is the corresponding empirical distribution. Suppose that T is Fisher consistent, i.e. T ( H$_{θ}$ ) = θ . The influence function of T , introduced by Hampel [9], measures the effect on the functional of a small fraction of point mass contamination. If δ$_{z}$ denotes the probability distribution that assigns mass 1 to x , then the influence function is defined by In our case, z = ( y $^{′}$, x $^{′}$)′ satisfy the linear model (1.1), θ = ( B$_{0}$ , Σ$_{0}$ ) and H$_{θ}$ = H$_{0}$ . Let T$_{0}$$_{,}$$_{1}$ , T$_{0}$$_{,}$$_{2}$ be the functional estimates asociated to the inicial estimates ˜ B$_{n}$ and ˜ Σ$_{n}$ , and T$_{1}$ , T$_{2}$ the functional estimates corresponding to the MM-estimates ̂ B$_{n}$ and ̂ Σ$_{n}$ . Then, according to (2.10) and (2.11), given a distribution function H of ( y $^{′}$, x $^{′}$)$^{′}$, the pair ( T$_{1}$ ( H ) , T$_{2}$ ( H )) is the value of ( B , Σ ) satisfying and E$_{H}$W ( d ( B , Σ )) ̂ u ( B ) x ′ = 0 , Σ = q E$_{H}$W ( d ( B , Σ )) ̂ u ( B ) ̂ u ( B ) ′ E$_{H}$$_{0}$ψ$_{1}$ ( d ( B , Σ )) d ( B , Σ ) , Σ = S ( H ) $^{2}$Γ , with | Γ | = 1 , 10 IF ( z , T , θ ) = lim ε → 0 T ((1 − ε ) H$_{θ}$ + εδ$_{z}$ ) − T ( H$_{θ}$ ) ε = ∂ T ((1 − ε ) H$_{θ}$ + εδ$_{z}$ ) ∂ε ∣ ε =0 , 4 Influence function