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Inference on the Order of a Normal Mixture


  • Jiahua Chen
  • Pengfei Li
  • Yuejiao Fu


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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    Cited by:

    1. 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.
    2. Maciejowska, Katarzyna, 2013. "Assessing the number of components in a normal mixture: an alternative approach," MPRA Paper 50303, University Library of Munich, Germany.
    3. Brennan, Timothy J., 2015. "Holding distribution utilities liable for outage costs," Energy Economics, Elsevier, vol. 48(C), pages 89-96.
    4. 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.

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