The likelihood ratio test for general mixture models with or without structural parameter

Jean-Marc Azaïs; Élisabeth Gassiat; Cécile Mercadier

ESAIM: Probability and Statistics (2009)

  • Volume: 13, page 301-327
  • ISSN: 1292-8100

Abstract

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This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations in a finite mixture with or without structural parameter.

How to cite

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Azaïs, Jean-Marc, Gassiat, Élisabeth, and Mercadier, Cécile. "The likelihood ratio test for general mixture models with or without structural parameter." ESAIM: Probability and Statistics 13 (2009): 301-327. <http://eudml.org/doc/250649>.

@article{Azaïs2009,
abstract = { This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations in a finite mixture with or without structural parameter. },
author = {Azaïs, Jean-Marc, Gassiat, Élisabeth, Mercadier, Cécile},
journal = {ESAIM: Probability and Statistics},
keywords = {Likelihood ratio test; mixture models; number of components; local power; contiguity; likelihood ratio test; number of components},
language = {eng},
month = {7},
pages = {301-327},
publisher = {EDP Sciences},
title = {The likelihood ratio test for general mixture models with or without structural parameter},
url = {http://eudml.org/doc/250649},
volume = {13},
year = {2009},
}

TY - JOUR
AU - Azaïs, Jean-Marc
AU - Gassiat, Élisabeth
AU - Mercadier, Cécile
TI - The likelihood ratio test for general mixture models with or without structural parameter
JO - ESAIM: Probability and Statistics
DA - 2009/7//
PB - EDP Sciences
VL - 13
SP - 301
EP - 327
AB - This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations in a finite mixture with or without structural parameter.
LA - eng
KW - Likelihood ratio test; mixture models; number of components; local power; contiguity; likelihood ratio test; number of components
UR - http://eudml.org/doc/250649
ER -

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