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The likelihood ratio test for the number of components in a mixture with Markov regime. (English) Zbl 0982.62016

Summary: 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.

MSC:

62F05 Asymptotic properties of parametric tests
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62M02 Markov processes: hypothesis testing
62M99 Inference from stochastic processes
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