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order of a mixture.

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The likelihood ratio test for the number of componentsin amixture with Markov regime
Elisabeth Gassiat, Christine Keribin
Journal:

ESAIM: Probability and Statistics / Volume 4 / 2000

Published online by Cambridge University Press:

15 August 2002, pp. 25-52

Print publication:

2000
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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.