Inference on the Order of a Normal Mixture
AbstractFinite 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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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.
Volume (Year): 107 (2012)
Issue (Month): 499 (September)
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- Hiroyuki Kasahara & Katsumi Shimotsu, 2012.
"Testing the Number of Components in Finite Mixture Models,"
CIRJE-F-867, CIRJE, Faculty of Economics, University of Tokyo.
- 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.
- 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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