Strongly consistent model selections for densities
Résumé
Let f be an unknown multivariate density belonging to a set of densities Fk! of finite associated Vapnik-Chervonenkis dimension, where the complexity k! is unknown, and Fk ! Fk+1 for all k. Given an i.i.d. sample of size n drawn from f, this article presents a density estimate ˆ fKn yielding almost sure convergence of the estimated complexity Kn to the true but unknown k!, and with the property E{ ! | ˆ fKn − f|} = O(1/#n). The methodology is inspired by the combinatorial tools developed in Devroye and Lugosi [8] and it includes a wide range of density models, such as mixture models and exponential families.
Origine | Fichiers produits par l'(les) auteur(s) |
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