# 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

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topAzaïs, 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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