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Abstract: The subject of this Note is to establish a functional large deviations principle for the process indexed by a family of functions and to deduce large deviations results in an unified way for the density and regression functions in the nonparametric estimation problem. Our results are then applied to model selection. To cite this article: D. Louani, S.M. Ould Maouloud, C. R. Acad. Sci. Paris, Ser. I 344 (2007). [Copyright &y& Elsevier]

Abstract: We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and Gaussian noise. The estimation of the parameters of the MLP can be made by maximizing the likelihood of the model. In this framework, it is difficult to determine the true number of hidden units because the information matrix of Fisher is not invertible if this number is overestimated. However, if the parameters of the MLP are in a compact set, we prove that the minimization of a suitable information criteria leads to consistent estimation of the true number of hidden units. To cite this article: J. Rynkiewicz, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]

Abstract: We obtain rates of strong uniform consistency for some nonparametric regression estimators, including the local linear regression and some wavelet estimators. Our method of proof relies on recent empirical process theory developed by Deheuvels and Mason (Statist. Inference Stoch. Process. 7 (3) (2004) 225–277). To cite this article: D. Blondin et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: We study a class of nonlinear regression models for scalar or vectorial response when the explanatory variable is a function. We introduce a consistent estimator of the parameters of models in this class when functions are evaluated at randomly chosen observation points. To cite this article: F. Rossi, B. Conan-Guez, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: In the setting of the additive model of the regression function, we study the iterated logarithm law for this model components pertaining with the marginal integration estimation method. Our results are stated in the i.i.d. random vectors framework. To cite this article: M. Debbarh, C. R. Acad. Sci. Paris, Ser. I 339 (2004). [Copyright &y& Elsevier]

Abstract: We establish uniform consistency rates for Nadaraya–Watson kernel-type estimators of the regression derivatives in a multidimensional framework. Our methods are based upon modern empirical process theory in the spirit of Deheuvels and Mason [Stat. Inference Stoch. Process. 7 (2004)] with respect to uniform deviations of nonparametric estimators. To cite this article: D. Blondin, C. R. Acad. Sci. Paris, Ser. I 339 (2004). [Copyright &y& Elsevier]