Non linear wavelet density estimation on the real line
Résumé
We investigate the problem of density estimation on the real line $\mathbb{R}$ under $\mathbb{L}^1$ loss. We carry out a new way to select the important coefficients in some wavelet expansions. We study the resulting estimator when the density is smooth with dominated tails. These assumptions are very mild and allow in particular to deal with singularities, spatially inhomogeneous smoothness, and fat tailed distributions. Moreover, our estimator is fully adaptive and is derived from a computationally efficient algorithm.
Domaines
Statistiques [math.ST]Origine | Fichiers produits par l'(les) auteur(s) |
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