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Article Dans Une Revue Test Année : 2008

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.
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Dates et versions

hal-00456079 , version 1 (11-02-2010)

Identifiants

  • HAL Id : hal-00456079 , version 1

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Gérard Biau, Benoît Cadre, Luc Devroye, Laszlo Gyorfi. Strongly consistent model selections for densities. Test, 2008, pp.531-545. ⟨hal-00456079⟩
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