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sume that the partial derivatives of E$_{H}$$_{θ}$$_{1}$$_{,}$$_{θ}$$_{2}$ ( h$_{3}$ ( z , θ$_{1}$ , θ$_{2}$ , S ( θ , H$_{θ}$$_{1}$$_{,}$$_{θ}$$_{2}$ ))) can be ob- tained differentiating with respect to each parameter inside the expectation. Then the influence function of T$_{1}$ is given by 

Proof: Let H$_{ε}$ = (1 − ε ) H$_{θ}$$_{1}$$_{,}$$_{θ}$$_{2}$ + εδ$_{z}$$_{0}$ . Then T ( H$_{ε}$ ) satisfy 

<img src='content_image/319640.jpg'>

<img src='content_image/319641.jpg'>

The proof of the Lemma follows immediately differentiating the above expression with respect to ε in ε = 0 and using (A.25) and (A.26). ■ 

The following proves for the case Σ$_{0}$ = I that the functional MM-estimates T$_{1}$ and T$_{2}$ /S 2 are Fisher consistent for B$_{0}$ and I , respectively. 

Lemma 12. Let z = ( y $^{′}$, x $^{′}$)′ be a random vector that satisfy the MLM (1.1) with parameters B$_{0}$ and Σ$_{0}$ = I , where x satisfies (A2) and the distribution of u = y − B$_{0}$x satisfies (A3). Let ρ$_{1}$ be a ρ -function that satisfies (A1) and Σ ̸ = I such that | Σ | = 1 . Then 

<img src='content_image/319638.jpg'>

This lemma follows immediately from Lemma A.10 of [8]. 

