Consistency of M estimates for separable nonlinear regression models Mar´ıa Victoria Fasano 1 (virfeather@yahoo.com.ar) Ricardo Maronna 1 (rmaronna@retina.ar) $^{1}$Departamento de Matem´ atica, Facultad de Ciencias Exactas, Universidad de La Plata, C.C. 172, La Plata 1900, Argentina. Consider a nonlinear regression model : y$_{i}$ = g ( x$_{i}$ , θ ) + e$_{i}$, i = 1 , ..., n, where the x$_{i}$ are random predictors x$_{i}$ and θ is the unknown parameter vector ranging in a set Θ$_{⊂}$ R $^{p}$. All known results on the consistency of the least squares estimator and in general of M estimators assume that either Θ is compact or g is bounded, which excludes frequently employed models such as the Michaelis-Menten, logistic growth and exponential decay models. In this article we deal with the so-called separable models, where p = p$_{1}$ + p$_{2}$, θ = ( α, β ) with α ∈ A ⊂ R $^{p$_{1}$}$, β ∈ B ⊂ R p$_{2}$$^{,}$and g has the form g ( x , θ ) = β $^{T}$h ( x , α ) where h is a function with values in R $^{p$_{2}$}$. We prove the strong consistency of M estimators under very general assumptions, assuming that h is a bounded function of α, which includes the three models mentioned above. Key words and phrases: Nonlinear regression, separable models, con- sistency, robust estimation. arXiv:1207.0473v1 [math.ST] 2 Jul 2012 Abstract 1