Estimation and tests in finite mixture models of nonparametric densities

Odile Pons

ESAIM: Probability and Statistics (2009)

  • Volume: 13, page 276-282
  • ISSN: 1292-8100

Abstract

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The aim is to study the asymptotic behavior of estimators and tests for the components of identifiable finite mixture models of nonparametric densities with a known number of components. Conditions for identifiability of the mixture components and convergence of identifiable parameters are given. The consistency and weak convergence of the identifiable parameters and test statistics are presented for several models.

How to cite

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Pons, Odile. "Estimation and tests in finite mixture models of nonparametric densities." ESAIM: Probability and Statistics 13 (2009): 276-282. <http://eudml.org/doc/250666>.

@article{Pons2009,
abstract = { The aim is to study the asymptotic behavior of estimators and tests for the components of identifiable finite mixture models of nonparametric densities with a known number of components. Conditions for identifiability of the mixture components and convergence of identifiable parameters are given. The consistency and weak convergence of the identifiable parameters and test statistics are presented for several models. },
author = {Pons, Odile},
journal = {ESAIM: Probability and Statistics},
keywords = {Mixture models; nonparametric densities; test; weak convergence; mixture models},
language = {eng},
month = {7},
pages = {276-282},
publisher = {EDP Sciences},
title = {Estimation and tests in finite mixture models of nonparametric densities},
url = {http://eudml.org/doc/250666},
volume = {13},
year = {2009},
}

TY - JOUR
AU - Pons, Odile
TI - Estimation and tests in finite mixture models of nonparametric densities
JO - ESAIM: Probability and Statistics
DA - 2009/7//
PB - EDP Sciences
VL - 13
SP - 276
EP - 282
AB - The aim is to study the asymptotic behavior of estimators and tests for the components of identifiable finite mixture models of nonparametric densities with a known number of components. Conditions for identifiability of the mixture components and convergence of identifiable parameters are given. The consistency and weak convergence of the identifiable parameters and test statistics are presented for several models.
LA - eng
KW - Mixture models; nonparametric densities; test; weak convergence; mixture models
UR - http://eudml.org/doc/250666
ER -

References

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  2. K. Fukumizu, Likelihood ratio of unidendifiable models and multilayer neural networks, Ann. Statist.31 (2003) 833–851.  Zbl1032.62020
  3. J.K. Ghosh and P.K. Sen, On the aymptotic performance of the log-likelihood ratio statistic for the mixture model and related results. In Proc. of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, volume II, edited by L.M. Le Cam and R.A. Olshen, (1985), pp. 789–806.  
  4. M. Lemdani and O. Pons, Likelihood ratio tests in mixture models. C. R. Acad. Sci. Paris, Ser. I322 (1995) 399–404.  Zbl0842.62011
  5. M. Lemdani and O. Pons, Likelihood ratio tests in contamination models, Bernoulli5 (1999) 705–719.  Zbl0929.62015
  6. X. Liu and Y. Shao, Asymptotics for likelihood ratio tests under loss of identifiability, Ann. Statist.31 (2003) 807–832.  Zbl1032.62014
  7. O. Pons, Estimation et tests dans les modèles de mélanges de lois et de ruptures. Hermès-Science Lavoisier, London and Paris (2009).  
  8. A. Wald, Note on the consistency of the maximum likelihood estimate, Ann. Math. Statist.20 (1949) 595–601.  Zbl0034.22902

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