Estimation and tests in finite mixture models of nonparametric densities

Issue		ESAIM: PS Volume 13, 2009


Page(s)		276 - 282
DOI		10.1051/ps:2008014
Published online		04 July 2009

ESAIM: PS, July 2009, Vol. 13, p. 276-282
DOI: 10.1051/ps:2008014

Estimation and tests in finite mixture models of nonparametric densities

Odile Pons

pons.odile@free.fr

Received April 25, 2007. Revised January 16, 2008. Published online 4 July 2009

Abstract
The aim is to study the asymptotic behavior of estimators and tests for the components of identifiable finite mixture models of nonparametric densities with a known number of components. Conditions for identifiability of the mixture components and convergence of identifiable parameters are given. The consistency and weak convergence of the identifiable parameters and test statistics are presented for several models.

Résumé
Dans les modèles de mélanges de densités non paramétriques, une question est de déterminer le comportement asymptotique d'estimateurs et de statistiques de test sur les composantes identifiables. Des modèles de mélanges non paramétriques d'un nombre connu de densités sont considérés. Des conditions pour l'identifiabilité et pour les convergences des paramètres et fonctions identifiables sont présentées. Le comportement des statistiques de test est décrit et des estimateurs des composantes des densités sont définis dans plusieurs cas.

Mathematics Subject Classification. 62G10, 62H10

Key words: Mixture models, nonparametric densities, test, weak convergence

© EDP Sciences, SMAI 2009

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