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 On adaptive wavelet estimation of a class of weighted densities
 We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples, including those arising in order statistics or when $g$ is related to the maximum or the minimum of $N$ (random or fixed) independent and identically distributed (\iid) random variables. We here construct a new adaptive non-parametric estimator for $g$ based on a plug-in approach and the wavelets methodology. For a wide class of models, we prove that it attains fast rates of convergence under the $\mathbb{L}_p$ risk with $p\ge 1$ (not only for $p = 2$ corresponding to the mean integrated squared error) over Besov balls. The theoretical findings are illustrated through several simulations.
 Équipe de recherche : image
 Mots Clés : Weighted density – density estimation – plug-in approach – wavelets – block thresholding – reliability – series system – parallel system.
 hal-00714507, version 1 http://hal.archives-ouvertes.fr/hal-00714507 oai:hal.archives-ouvertes.fr:hal-00714507 Contributeur : Fabien Navarro <> Soumis le : Mercredi 4 Juillet 2012, 18:27:25 Dernière modification le : Mercredi 4 Juillet 2012, 19:15:23