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Testing the Order of Multivariate Normal Mixture Models

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  • Hiroyuki Kasahara

    (Vancouver School of Economics, University of British Columbia)

  • Katsumi Shimotsu

    (Faculty of Economics, The University of Tokyo)

Abstract

Testing the number of components in multivariate normal mixture models is a long-standing challenge. This paper develops a likelihood-based test of the null hypothesis of M 0 components against the alternative hypothesis of M 0 + 1 components. We derive a local quadratic approximation of the likelihood ratio statistic in terms of the polynomials of the parameters. Based on this quadratic approximation, we propose an EM test of the null hypothesis of M 0 components against the alternative hypothesis of M 0 + 1 components, and derive the asymptotic distribution of the proposed test statistic. The simulations show that the proposed test has good finite sample size and power properties.

Suggested Citation

  • Hiroyuki Kasahara & Katsumi Shimotsu, 2017. "Testing the Order of Multivariate Normal Mixture Models," CIRJE F-Series CIRJE-F-1044, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2017cf1044
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    References listed on IDEAS

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    1. Jiahua Chen & Pengfei Li & Yuejiao Fu, 2012. "Inference on the Order of a Normal Mixture," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1096-1105, September.
    2. Lemdani, Mohamed & Pons, Odile, 1997. "Likelihood ratio tests for genetic linkage," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 15-22, April.
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    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.
    5. Hiroyuki Kasahara & Katsumi Shimotsu, 2015. "Testing the Number of Components in Normal Mixture Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1632-1645, December.
    6. Hanfeng Chen & Jiahua Chen & John D. Kalbfleisch, 2004. "Testing for a finite mixture model with two components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 95-115, February.
    7. Chen, Jiahua & Tan, Xianming, 2009. "Inference for multivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1367-1383, August.
    8. Li, Pengfei & Chen, Jiahua, 2010. "Testing the Order of a Finite Mixture," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1084-1092.
    9. Hong‐Tu Zhu & Heping Zhang, 2004. "Hypothesis testing in mixture regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 3-16, February.
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    Cited by:

    1. Paul Schrimpf & Michio Suzuki & Hiroyuki Kasahara, 2015. "Identification and Estimation of Production Function with Unobserved Heterogeneity," 2015 Meeting Papers 924, Society for Economic Dynamics.
    2. Yu Hao & Hiroyuki Kasahara, 2022. "Testing the Number of Components in Finite Mixture Normal Regression Model with Panel Data," Papers 2210.02824, arXiv.org, revised Jun 2023.

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