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Inference on the Order of a Normal Mixture

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  • Jiahua Chen
  • Pengfei Li
  • Yuejiao Fu

Abstract

Finite normal mixture models are used in a wide range of applications. Hypothesis testing on the order of the normal mixture is an important yet unsolved problem. Existing procedures often lack a rigorous theoretical foundation. Many are also hard to implement numerically. In this article, we develop a new method to fill the void in this important area. An effective expectation-maximization (EM) test is invented for testing the null hypothesis of arbitrary order m 0 under a finite normal mixture model. For any positive integer m 0 ⩾ 2, the limiting distribution of the proposed test statistic is . We also use a novel computer experiment to provide empirical formulas for the tuning parameter selection. The finite sample performance of the test is examined through simulation studies. Real-data examples are provided. The procedure has been implemented in R code. The p -values for testing the null order of m 0 = 2 or m 0 = 3 can be calculated with a single command. This article has supplementary materials available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1096-1105
    DOI: 10.1080/01621459.2012.695668
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    Citations

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    Cited by:

    1. Michael Vogt & Matthias Schmid, 2021. "Clustering with statistical error control," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 729-760, September.
    2. Wang Miao & Peng Ding & Zhi Geng, 2016. "Identifiability of Normal and Normal Mixture Models with Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1673-1683, October.
    3. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Testing the Number of Components in Finite Mixture Models," CIRJE F-Series CIRJE-F-867, CIRJE, Faculty of Economics, University of Tokyo.
    4. Wichitchan, Supawadee & Yao, Weixin & Yang, Guangren, 2019. "Hypothesis testing for finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 180-189.
    5. Maciejowska, Katarzyna, 2013. "Assessing the number of components in a normal mixture: an alternative approach," MPRA Paper 50303, University Library of Munich, Germany.
    6. Holzmann, Hajo & Schwaiger, Florian, 2016. "Testing for the number of states in hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 318-330.
    7. Hiroyuki Kasahara & Katsumi Shimotsu, 2018. "Testing the Number of Regimes in Markov Regime Switching Models," Papers 1801.06862, arXiv.org, revised Jan 2018.
    8. Brennan, Timothy J., 2015. "Holding distribution utilities liable for outage costs," Energy Economics, Elsevier, vol. 48(C), pages 89-96.
    9. Bagkavos, Dimitrios & Patil, Prakash N., 2023. "Goodness-of-fit testing for normal mixture densities," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    10. 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.
    11. Yanyuan Ma & Shaoli Wang & Lin Xu & Weixin Yao, 2021. "Semiparametric mixture regression with unspecified error distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 429-444, June.
    12. Yin, Cuihong & Sheldon Lin, X. & Huang, Rongtan & Yuan, Haili, 2019. "On the consistency of penalized MLEs for Erlang mixtures," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 12-20.
    13. Xu Gao & Weining Shen & Jing Ning & Ziding Feng & Jianhua Hu, 2022. "Addressing patient heterogeneity in disease predictive model development," Biometrics, The International Biometric Society, vol. 78(3), pages 1045-1055, September.
    14. 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).

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