LIKELIHOOD RATIO TESTS IN MIXTURE-MODELS

The classical theory on the asymptotic distribution of the likelihood ratio statistic fails for testing whether a mixture of p + q distribut ions of the same parametric form reduces to a mixture of p distributio ns. We propose a general reparametrization method which ensures regula rity properties. Under the null hypothesis, the LR statistic then conv erges to the supremum of a square truncated Gaussian process.