Inference on the Order of a Normal Mixture

Jiahua Chen, Pengfei Li and Yuejiao Fu

Journal of the American Statistical Association, 2012, vol. 107, issue 499, 1096-1105

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.

Date: 2012
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Citations: View citations in EconPapers (16)

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DOI: 10.1080/01621459.2012.695668

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