Estimation and tests in finite mixture models of nonparametric densities
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 276-282.

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.

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.

DOI : 10.1051/ps:2008014
Classification : 62G10, 62H10
Mots clés : mixture models, nonparametric densities, test, weak convergence 
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Pons, Odile. Estimation and tests in finite mixture models of nonparametric densities. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 276-282. doi : 10.1051/ps:2008014. http://www.numdam.org/articles/10.1051/ps:2008014/

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