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The likelihood ratio test for the number of components in a mixture with Markov regime

Published online by Cambridge University Press:  15 August 2002

Elisabeth Gassiat  and
Christine Keribin
Elisabeth Gassiat
Affiliation:
Laboratoire Modélisation Stochastique et Statistique, Université d'Orsay, bâtiment 425, 91405 Orsay, France; Elisabeth.Gassiat@math.u-psud.fr.
Christine Keribin
Affiliation:
Laboratoire Modélisation Stochastique et Statistique, Université d'Orsay, bâtiment 425, 91405 Orsay, France; Elisabeth.Gassiat@math.u-psud.fr.
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Abstract

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.

Keywords

Likelihood ratio testhidden Markov modelorder of a mixture.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 4 , 2000 , pp. 25 - 52
Copyright
© EDP Sciences, SMAI, 2000

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