Inégalités d'oracle pour l'estimation d'une densité de probabilité

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Abstract

We study the problem of the nonparametric estimation of a probability density in L2(ℝ). Expressing the mean integrated squared error in the Fourier domain, we show that it is close to the mean integrated squared error in the Gaussian sequence model. Then, applying a modified version of Stein's blockwise method, we obtain a linear monotone oracle inequality and a kernel oracle inequality. As a consequence, the proposed estimator is sharp minimax adaptive (i.e. up to a constant) on a scale of Sobolev classes of densities. © 2004 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés.

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Rigollet, P. (2005). Inégalités d’oracle pour l’estimation d’une densité de probabilité. Comptes Rendus Mathematique, 340(1), 59–62. https://doi.org/10.1016/j.crma.2004.11.009

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