Free Access
Issue
ESAIM: PS
Volume 13, January 2009
Page(s) 301 - 327
DOI https://doi.org/10.1051/ps:2008010
Published online 21 July 2009
  1. R.J. Adler, An introduction to continuity, extrema and related topics for general Gaussian processes. Inst. Math. Statist. Lect. Notes-Monograph Ser. 12 (1990). [Google Scholar]
  2. J.-M. Azais, E. Gassiat C. and Mercadier, Asymptotic distribution and power of the likelihood ratio test for mixtures: bounded and unbounded case. Bernoulli 12 (2006) 775–799. [CrossRef] [MathSciNet] [Google Scholar]
  3. P.J. Bickel, C.A.J. Klaassen, Y. Ritov and J.A. Wellner, Efficient and adaptive estimation for semiparametric models. Johns Hopkins Series in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, MD (1993). [Google Scholar]
  4. A. Chambaz, Testing the order of a model. Ann. Statist. 34 (2006) 1166–1203. [Google Scholar]
  5. A. Chambaz, A. Garivier and E. Gassiat, A mdl approach to hmm with Poisson and Gaussian emissions. Application to order identification. Submitted (2005). [Google Scholar]
  6. H. Chen and J. Chen, Large sample distribution of the likelihood ratio test for normal mixtures, Statist. Probab. Lett. 2 (2001) 125–133. [Google Scholar]
  7. H. Chen and J. Chen, Test for homogeneity in normal mixtures in the presence of a structural parameter. Statist. Sinica 13 (2003) 355–365. [Google Scholar]
  8. J. Chen and J.D. Kalbfleisch, Modified likelihood ratio test in finite mixture models with a structural parameter. J. Stat. Planning Inf. 129 (2005) 93–107. [CrossRef] [Google Scholar]
  9. H. Chen, J. Chen and J.D. Kalbfleisch, A modified likelihood ratio test for homogeneity in finite mixture models. J. Roy. Statist. Soc. B 63 (2001) 19–29. [CrossRef] [Google Scholar]
  10. H. Chen, J. Chen and J.D. Kalbfleisch, Testing for a finite mixture model with two components. J. Roy. Statist. Soc. B 66 (2004) 95–115. [CrossRef] [Google Scholar]
  11. H. Chernoff and E. Lander, Asymptotic distribution of the likelihood ratio test that a mixture of two binomials is a single binomial. J. Stat. Planning Inf. 43 (1995) 19–40. [CrossRef] [Google Scholar]
  12. T. Chihara, An introduction to orthogonal polynomials. Gordon and Breach, New York (1978). [Google Scholar]
  13. G. Ciuperca, Likelihood ratio statistic for exponential mixtures. Ann. Inst. Statist. Math. 54 (2002) 585–594. [CrossRef] [MathSciNet] [Google Scholar]
  14. D. Dacunha-Castelle and E. Gassiat, Testing in locally conic models, and application to mixture models. ESAIM Probab. Statist. 1 (1997) 285–317. [Google Scholar]
  15. D. Dacunha-Castelle and E. Gassiat, Testing the order of a model using locally conic parameterization: population mixtures and stationary ARMA processes. Ann. Statist. 27 (1999) 1178–1209. [Google Scholar]
  16. C. Delmas, On likelihood ratio test in Gaussian mixture models, Sankya 65 (2003) 513-531. [Google Scholar]
  17. B. Garel, Likelihood Ratio Test for Univariate Gaussian Mixture. J. Statist. Planning Inf. 96 (2001) 325–350. [CrossRef] [Google Scholar]
  18. B. Garel, Asymptotic theory of the likelihood ratio test for the identification of a mixture. J. Statist. Planning Inf. 131 (2005) 271–296. [CrossRef] [Google Scholar]
  19. E. Gassiat, Likelihood ratio inequalities with applications to various mixtures. Ann. Inst. H. Poincaré Probab. Statist. 6 (2002) 897–906. [Google Scholar]
  20. E. Gassiat and C. Keribin, The likelihood ratio test for the number of components in a mixture with Markov regime, 2000. ESAIM Probab. Stat. 4 (2000) 25–52. [Google Scholar]
  21. J. Ghosh and P. Sen, On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results, Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Vol. II. Wadsworth, Belmont, CA (1985) 789–806. [Google Scholar]
  22. P. Hall and M. Stewart, Theoretical analysis of power in a two-component normal mixture model. J. Statist. Planning Inf. 134 (2005) 158–179. [CrossRef] [Google Scholar]
  23. J.A. Hartigan, A failure of likelihood asymptotics for normal mixtures, In Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer (Berkeley, CA, 1983), Vol. II. Wadsworth, Belmont, CA (1985) 807–810. [Google Scholar]
  24. J. Henna, Estimation of the number of components of finite mixtures of multivariate distributions. Ann. Inst. Statist. Math. 57 (2005) 655–664. [CrossRef] [MathSciNet] [Google Scholar]
  25. L.F. James, C.E. Priebe and D.J. Marchette, Consistent Estimation of Mixture Complexity. Ann. Statist. 29 (2001) 1281–1296. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Keribin, Consistent estimation of the order of mixture models. Sankhyā Ser. A 62 (2000) 49–66. [Google Scholar]
  27. M. Lemdani and O. Pons, Likelihood ratio test for genetic linkage. Statis. Probab. Lett. 33 (1997) 15–22. [CrossRef] [Google Scholar]
  28. M. Lemdani and O. Pons, Likelihood ratio in contamination models. Bernoulli 5 (1999) 705–719. [CrossRef] [MathSciNet] [Google Scholar]
  29. B.G. Lindsay, Mixture models: Theory, geometry, and applications. NSF-CBMS Regional Conf. Ser. Probab. Statist., Vol. 5. Hayward, CA, Institute for Mathematical Statistics (1995). [Google Scholar]
  30. X. Liu and Y. Shao, Asymptotics for the likelihood ratio test in two-component normal mixture models. J. Statist. Planning Inf. 123 (2004) 61–81. [CrossRef] [Google Scholar]
  31. X. Liu, C. Pasarica and Y. Shao, Testing homogeneity in gamma mixture models. Scand. J. Statist. 30 (2003) 227–239. [CrossRef] [MathSciNet] [Google Scholar]
  32. Y. Lo, Likelihood ratio tests of the number of components in a normal mixture with unequal variances. Statis. Probab. Lett. 71 (2005) 225–235. [CrossRef] [Google Scholar]
  33. F. Lord, Estimating the true-score distributions in psychological testing (an empirical bayes estimation problem). Psychometrika 34 (1969) 259–299. [CrossRef] [Google Scholar]
  34. G. McLachlan and D. Peel, Finite mixture models Wiley Series in Probability and Statistics: Applied Probability and Statistics. Wiley-Interscience, New York (2000). [Google Scholar]
  35. C. Mercadier (2005), toolbox MATLAB. http://www.math.univ-lyon1.fr/mercadier/MAGP/ [Google Scholar]
  36. N. Misra, H. Singh and E.J. Harner, Stochastic comparisons of poisson and binomial random varaibles with their mixtures. Statist. Probab. Lett. 65 279–290. [Google Scholar]
  37. S.A. Murphy and A.W. van der Vaart, Semiparametric likelihood ratio inference. Ann. Statist. 25 (1997) 1471–1509. [CrossRef] [MathSciNet] [Google Scholar]
  38. Y.S. Quin and B. Smith, Likelihood ratio test for homogeneity in normal mixtures in the presence of a structural parameter. Statist. Sinica 143 (2004) 1165–1177. [Google Scholar]
  39. Y.S. Quin and B. Smith, The likelihood ratio test for homogeneity in bivariate normal mixtures. J. Multivariate Anal. 97 (2006) 474–491. [CrossRef] [MathSciNet] [Google Scholar]
  40. D.M. Titterington, A.F.M. Smith and U.E. Makov, Statistical analysis of finite mixture distributions. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, Ltd (1985). [Google Scholar]
  41. A.W. van der Vaart and J.A. Wellner, Weak convergence and empirical processes, Springer Ser. Statist. Springer-Verlag (1996). [Google Scholar]
  42. A.W. van der Vaart, Asymptotic statistics, Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (1998). [Google Scholar]
  43. A.W. van der Vaart, Semiparametric Statistics, Lectures on probability theory and statistics, Saint-Flour, 1999. Lect. Notes Math. 1781 331–457. Springer, Berlin (2002). [Google Scholar]
  44. G.R. Wood, Binomial mixtures: geometric estimation of the mixing distribution. Ann. Statist. 5 (1999) 1706–1721. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.