This paper deals with the likelihood ratio test (LRT) for testing hypotheseson the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRTstatisticsunder some conditions that are proved to be almost necessary.A detailed solution is given for two testing problems: thetest of a single distribution against any mixture, with application to Gaussian, Poisson andbinomial distributions; the test of the number of populations in afinite mixture with or without structural parameter.
