where ρ is a loss function whose properties will be described in the next section and ̂ σ is an estimate of the error’s scale. However, at this stage of our research we deal with the simpler case of known σ. Then it may be assumed without loss of generality that σ = 1 and therefore we shall deal with estimates of the form All published results on the consistency of robust estimates for nonlinear The well-known fact that the LSE is sensitive to outliers has led to the devel- opment of robust estimates that are simultaneously highly efficient for normal errors and resistant to perturbations of the model. One of the most important families of robust estimates are the M-estimates proposed by Huber (1973) for the linear model. For nonlinear models they are defined by assumes that Θ is a finite set. Richardson and Bhattacharyya (1986) do not require the compactness of Θ , but they assume g ( x , θ ) to be a bounded function of θ, which excludes most separable models. Shao (1992) showed the consistency of the LSE without requiring the com- pacity of Θ nor the boundedness of g, but requires assumptions on g that exclude the simplest separable models. For example, in the case g ( x, θ ) = βe $^{αx}$, for any x$_{0}$ > 0 one can make g ( x$_{0}$, θ ) =constant with α → −∞ and β → 0 . This fact violates both “Condition 1” and “Condition 2” in page 427 of his paper. The consistency of the LSE assuming E ( e$_{i}$ ) = 0 and Var ( e$_{i}$ ) = σ 2 < ∞ has been proved by several authors under the assumption of a compact Θ; in particular Amemiya (1983), Jennrich (1969) and Johansen (1984). Wu (1981) ˆ θ$_{n}$ = arg min θ ∈ Θ n ∑ i =1 ρ ( y$_{i}$ − g ( x$_{i}$ , θ ) ̂ σ ) , (6) ˆ θ$_{n}$ = arg min θ ∈ Θ n ∑ i =1 ρ ( y$_{i}$ − g ( x$_{i}$ , θ )) . (7) 3