Estimating composite functions by model selection

Abstract : We consider the problem of estimating a function s on [−1,1]k for large values of k by looking for some best approximation of s by composite functions of the form g ◦ u. Our solution is based on model selection and leads to a very general approach to solve this problem with respect to many different types of functions g, u and statistical frameworks. In particular, we handle the problems of approximating s by additive functions, single and multiple index models, neural networks, mixtures of Gaussian densities (when s is a density) among other examples. We also investigate the situation where s = g ◦ u for functions g and u belonging to possibly anisotropic smoothness classes. In this case, our approach leads to a completely adaptive estimator with respect to the regularity of s.
Type de document :
Article dans une revue
Annales de l'Institut Henri Poincaré, 2013, pp.285-314
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Contributeur : Yannick Baraud <>
Soumis le : jeudi 22 novembre 2012 - 14:15:31
Dernière modification le : mercredi 21 mars 2018 - 18:56:48
Document(s) archivé(s) le : samedi 23 février 2013 - 03:44:46


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  • HAL Id : hal-00756061, version 1



Yannick Baraud, Lucien Birgé. Estimating composite functions by model selection. Annales de l'Institut Henri Poincaré, 2013, pp.285-314. 〈hal-00756061〉



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