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Non linear regression models are a standard tool for modeling real phenomena,with several applications in machine learning, ecology, econometry...Estimating the parameters of the model has garnered a lot of attention duringmany years. We focus here on a recursive method for estimating parameters ofnon linear regressions. Indeed, these kinds of methods, whose most famous areprobably the stochastic gradient algorithm and its averaged version, enable todeal efficiently with massive data arriving sequentially. Nevertheless, theycan be, in practice, very sensitive to the case where the eigen-values of theHessian of the functional we would like to minimize are at different scales. Toavoid this problem, we first introduce an online Stochastic Gauss-Newtonalgorithm. In order to improve the estimates behavior in case of badinitialization, we also introduce a new Averaged Stochastic Gauss-Newtonalgorithm and prove its asymptotic efficiency.

An efficient Averaged Stochastic Gauss-Newton algorithm for estimating parameters of non linear regressions models