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Likelihood ratio tests of the number of components in a normal mixture with unequal variances


  • Lo, Yungtai


Determining the number of components in a mixture distribution is of interest to researchers in many areas. In this paper, we investigate the statistical properties of a likelihood ratio test proposed by Lo et al. (Biometrika 88 (2001) 767) for determining the number of components in a normal mixture with unequal variances. We discuss the dependence of the rate of convergence of the likelihood ratio statistic to its limiting distribution on the choice of restrictions imposed on the component variances to deal with the problem of unboundedness of the likelihood. We compare the test procedure to the parametric bootstrap method and posterior predictive checks, a Bayesian model checking procedure.

Suggested Citation

  • Lo, Yungtai, 2005. "Likelihood ratio tests of the number of components in a normal mixture with unequal variances," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 225-235, March.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:3:p:225-235

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    References listed on IDEAS

    1. Phillips, Robert F., 1991. "A constrained maximum-likelihood approach to estimating switching regressions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 241-262.
    2. L. Wasserman, 2000. "Asymptotic inference for mixture models by using data-dependent priors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 159-180.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    4. Hanfeng Chen & Jiahua Chen & John D. Kalbfleisch, 2001. "A modified likelihood ratio test for homogeneity in finite mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 19-29.
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    Cited by:

    1. Lo, Yungtai, 2011. "Bias from misspecification of the component variances in a normal mixture," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2739-2747, September.
    2. Hung-Chia Chen & James J. Chen, 2016. "Hybrid Mixture Model for Subpopulation Identification," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(1), pages 28-42, June.


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