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| HAL : hal-00148063, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Nonparametric estimation of composite functions |
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| Anatoli Juditsky 1Oleg Lepski 2 |
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| (21/05/2007) |
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| We study the problem of nonparametric estimation of a multivariate function $g:\bR^d\to\bR$ that can be represented as a composition of two unknown smooth functions $f:\bR\to\bR$ and $G:\bR^d\to\bR$. We suppose that $f$ and $G$ belong to some known smoothness classes of functions and we construct an estimator of $g$ which is optimal in a minimax sense for the sup-norm loss. The proposed methods are based on aggregation of linear estimators associated to appropriate local structures, and the resulting procedures are nonlinear with respect to observations. |
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| 1 : | Laboratoire Jean Kuntzmann (LJK) |
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CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| 2 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 3 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00148063, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00148063 | |
| oai:hal.archives-ouvertes.fr:hal-00148063 | |
| Contributeur : Guillaume Lecué | |
| Soumis le : Lundi 21 Mai 2007, 20:00:37 | |
| Dernière modification le : Lundi 15 Avril 2013, 16:54:14 | |
