The likelihood ratio test for general mixture models with or without structural parameter

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

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Équipe Probabilités
3 Université de Lyon

This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without 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 or without structural parameter.

Mots clés: Mathematics

Jean-Marc Azaïs, Élisabeth Gassiat, Cécile Mercadier. The likelihood ratio test for general mixture models with or without structural parameter. ESAIM: Probability and Statistics, 2009, 13, pp.301-327. ⟨10.1051/ps:2008010⟩. ⟨hal-00504651v2⟩