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

Elisabeth Gassiat; Christine Keribin

ESAIM: Probability and Statistics (2010)

  • Volume: 4, page 25-52
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Gassiat, Elisabeth, and Keribin, Christine. "The likelihood ratio test for the number of components in a mixture with Markov regime." ESAIM: Probability and Statistics 4 (2010): 25-52. <http://eudml.org/doc/197725>.

@article{Gassiat2010,
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. },
author = {Gassiat, Elisabeth, Keribin, Christine},
journal = {ESAIM: Probability and Statistics},
keywords = {Likelihood ratio test; hidden Markov model; order of a mixture.; LRT statistic; mixture; Markov regime},
language = {eng},
month = {3},
pages = {25-52},
publisher = {EDP Sciences},
title = {The likelihood ratio test for the number of components in a mixture with Markov regime},
url = {http://eudml.org/doc/197725},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Gassiat, Elisabeth
AU - Keribin, Christine
TI - The likelihood ratio test for the number of components in a mixture with Markov regime
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 25
EP - 52
AB - 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.
LA - eng
KW - Likelihood ratio test; hidden Markov model; order of a mixture.; LRT statistic; mixture; Markov regime
UR - http://eudml.org/doc/197725
ER -

References

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