The likelihood ratio test for general mixture models with possibly unknown structural parameter

Jean-Marc Azaïs (1) , Elisabeth Gassiat (2) , Cécile Mercadier (3)

1 LSP - Laboratoire de Statistique et Probabilités
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 PSPM - Probabilités, statistique, physique mathématique

This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with possibly unknown structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations in a finite mixture with possibly unknown structural parameter.

Mots clés: mixture models; local power; contiguity; Likelihood ratio test; contiguity.; number of components

Domaines: Statistiques [math.ST]

Jean-Marc Azaïs, Elisabeth Gassiat, Cécile Mercadier. The likelihood ratio test for general mixture models with possibly unknown structural parameter. ESAIM: Probability and Statistics, 2009, 13, pp.301-327. ⟨10.1051/ps:2008010⟩. ⟨hal-00504651v1⟩