6 Asymptotic Normality Before obtaining the limit distribution of ̂ B$_{n}$ we need to make some additional assumptions. (A5) ρ$_{1}$ is differentiable, ψ$_{1}$ = ρ ′ 1 and W ( u ) = ψ$_{1}$ ( u ) /u is differentiable with bounded derivative. (A6) E$_{G}$$_{0}$ ‖ x ‖ 4 < ∞ , E$_{G}$$_{0}$ ‖ x ‖ 6 < ∞ , E$_{H}$$_{0}$ ‖ x ‖ $^{4}$‖ y ‖ 2 < ∞ and E$_{H}$$_{0}$ ‖ x ‖ $^{2}$‖ y ‖ 4 < ∞ , where H$_{0}$ is the distribution of z = ( y $^{′}$, x $^{′}$)$^{′}$. (A7) Let θ = ( B , Σ ) and The function Φ( θ ) = E$_{H}$$_{0}$φ ( z ; θ ) has a partial derivative ∂ Φ /∂ vec( B $^{′}$)′ which is continuous at θ$_{0}$ = ( B$_{0}$ , σ 2 $_{0}$Σ$_{0}$ ) and the matrix is non singular. Theorem 6. Let z$_{i}$ = ( y ′ $_{i}$, x $^{′}$$_{i}$) , with 1 ≤ i ≤ n , be a random sample from the model (1.1) with parameters B$_{0}$ and Σ$_{0}$ . Assume that the ρ -function ρ$_{1}$ satisfies (A1), that (A3)-(A7) hold and that the estimates ˜ B$_{n}$ and ˜ Σ$_{n}$ are consistent for B$_{0}$ and Γ$_{0}$ = Σ$_{0}$ | Σ$_{0}$ | − 1 /q respectively; then n 1 / $^{2}$vec ( ̂ B ′ n − B ′ $_{0}$) d → N$_{qp}$ ( 0 , V ) , where d → denotes convergence in distribution and where M is the covariance matrix φ ( z$_{1}$ , ( B$_{0}$ , σ 2 $_{0}$Σ$_{0}$ )) , with φ defined in (6.1) and 13 V = Λ − $^{1}$MΛ − 1 ′ (6.3) Λ = ∂ Φ( B , Σ ) ∂ vec( B $^{′}$)$_{′}$( B$_{0}$ , σ 2 $_{0}$Σ$_{0}$ ) (6.2) φ ( z ; θ ) = W ( d ( B , Σ )) vec(( y − B $^{′}$x ) x $^{′}$) . (6.1)