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Inference on the Order of a Normal Mixture

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  • Jiahua Chen
  • Pengfei Li
  • Yuejiao Fu
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    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.

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    File URL: http://hdl.handle.net/10.1080/01621459.2012.695668
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

    Volume (Year): 107 (2012)
    Issue (Month): 499 (September)
    Pages: 1096-1105

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    Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1096-1105

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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.

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