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Testing the Number of Components in Finite Mixture Models

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  • Kasahara Hiroyuki
  • Shimotsu Katsumi

Abstract

This paper considers likelihood-based testing of the null hypothesis of m0 components against the alternative of m0+1 components in a finite mixture model. The number of components is an important parameter in the applications of finite mixture models. Still, testing the number of components has been a long-standing challenging problem because of its non-regularity. We develop a framework that facilitates the analysis of the likelihood function of finite mixture models and derive the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of m0 components against the alternative of m0+1 components. Furthermore, building on this framework, we propose a likelihood-based testing procedure of the number of components. The proposed test, extending the EM approach of Li, Chen and Marriott (2009), does not use a penalty term and is implementable even when the likelihood ratio test is difficult to implement because of non-regularity and computational complexity.

Suggested Citation

  • Kasahara Hiroyuki & Shimotsu Katsumi, 2012. "Testing the Number of Components in Finite Mixture Models," Global COE Hi-Stat Discussion Paper Series gd12-259, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd12-259
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    Cited by:

    1. Yangguang Huang & Ming He, 2021. "Structural Analysis Of Tullock Contests With An Application To U.S. House Of Representatives Elections," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(3), pages 1011-1054, August.
    2. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.
    3. 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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