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