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Testing the Number of Components in Normal Mixture Regression Models

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  • Hiroyuki Kasahara
  • Katsumi Shimotsu

Abstract

Testing the number of components in finite normal mixture models is a long-standing challenge because of its nonregularity. This article studies likelihood-based testing of the number of components in normal mixture regression models with heteroscedastic components. We construct a likelihood-based test of the null hypothesis of m 0 components against the alternative hypothesis of m 0 + 1 components for any m 0 . The null asymptotic distribution of the proposed modified EM test statistic is the maximum of m 0 random variables that can be easily simulated. The simulations show that the proposed test has very good finite sample size and power properties. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1632-1645
    DOI: 10.1080/01621459.2014.986272
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    Citations

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    Cited by:

    1. Natalia Khorunzhina & Jean-François Richard, 2019. "Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 991-1017, March.
    2. Fisher, Mark & Jensen, Mark J., 2022. "Bayesian nonparametric learning of how skill is distributed across the mutual fund industry," Journal of Econometrics, Elsevier, vol. 230(1), pages 131-153.
    3. Dante Amengual & Xinyue Bei & Marine Carrasco & Enrique Sentana, 2022. "Score-type tests for normal mixtures," Working Papers wp2022_2213, CEMFI.
    4. Hiroyuki Kasahara & Katsumi Shimotsu, 2018. "Testing the Number of Regimes in Markov Regime Switching Models," Papers 1801.06862, arXiv.org, revised Jan 2018.
    5. 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.
    6. Krasnokutskaya, Elena & Song, Kyungchul & Tang, Xun, 2022. "Estimating unobserved individual heterogeneity using pairwise comparisons," Journal of Econometrics, Elsevier, vol. 226(2), pages 477-497.
    7. 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.
    8. Pan, Lanfeng & Li, Yehua & He, Kevin & Li, Yanming & Li, Yi, 2020. "Generalized linear mixed models with Gaussian mixture random effects: Inference and application," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    9. Paul Schrimpf & Michio Suzuki & Hiroyuki Kasahara, 2015. "Identification and Estimation of Production Function with Unobserved Heterogeneity," 2015 Meeting Papers 924, Society for Economic Dynamics.
    10. Wong, Tony S.T. & Lam, Kwok Fai & Zhao, Victoria X., 2018. "Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 248-257.
    11. 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.
    12. Wichitchan, Supawadee & Yao, Weixin & Yang, Guangren, 2019. "Hypothesis testing for finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 180-189.
    13. 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.
    14. Alexander D. Stead & Phill Wheat & William H. Greene, 2023. "On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model," Journal of Productivity Analysis, Springer, vol. 60(1), pages 37-48, August.

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