The likelihood ratio test for the number of components in a mixture with Markov regime
Élisabeth Gassiat, Christine Keribin · ESAIM Probability and Statistics · 2000
We study the LRT statistic for testing a single population i.i.d. model against a mixture of two populations with Markov regime. We prove that the LRT statistic converges to infinity in probability as the number of observations tends to infinity. This is a consequence of a convergence result of the LRT statistic for a subproblem where the parameters are restricted to a subset of the whole parameter set.