Strongly consistent model selection for densities

• Autores: Gérard Biau , Benoît Cadre, Luc Devroye , László Györfi
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 17, Nº. 3, 2008, págs. 531-545
• Idioma: inglés
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• Resumen

  • 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 ℱ k ⊂ℱ k+1 for all k. Given an i.i.d. sample of size n drawn from f, this article presents a density estimate f^Kn yielding almost sure convergence of the estimated complexity K n to the true but unknown k * and with the property E{∫|f^Kn−f|}=O(1/n−−√) . The methodology is inspired by the combinatorial tools developed in Devroye and Lugosi (Combinatorial methods in density estimation. Springer, New York, 2001) and it includes a wide range of density models, such as mixture models and exponential families.