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

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  • Lo, Yungtai

Abstract

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.

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  • 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

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    1. 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.
    2. 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.
    3. G. J. McLachlan, 1987. "On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 318-324, November.
    4. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. Phillips, Robert F., 1991. "A constrained maximum-likelihood approach to estimating switching regressions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 241-262.
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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. Ye, Mao & Lu, Zhao-Hua & Li, Yimei & Song, Xinyuan, 2019. "Finite mixture of varying coefficient model: Estimation and component selection," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 452-474.
    3. 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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