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Tuning the EM-test for finite mixture models

✍ Scribed by Jiahua Chen; Pengfei Li

Publisher
John Wiley and Sons
Year
2011
Tongue
French
Weight
152 KB
Volume
39
Category
Article
ISSN
0319-5724

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✦ Synopsis

Abstract

There has been rapid progress in developing effective and easy‐to‐use tests of the order of a finite mixture model. The EM‐test is the latest to join the rank. It has a relatively simple limiting distribution and enjoys broad applicability. Based on asymptotic theory, the P‐value of the EM‐test is approximated via its limiting distribution. The built‐in tuning parameter has an important influence on the approximation precision. Thus, choosing an appropriate value for this parameter is important for fully realizing the advantages of the EM‐test. In this article, we develop a novel computer‐experiment approach to address this issue. Through designed experiments, we derive a number of empirical formulas for the tuning parameter. Extensive validation simulation shows that these formulas work well in terms of providing accurate type I errors. The Canadian Journal of Statistics 39: 389–404; 2011 Β© 2011 Statistical Society of Canada

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The maximum-likelihood estimate of a mixture model is usually found by using the EM algorithm. However, the EM algorithm suffers from the local-optimum problem and therefore we cannot obtain the potential performance of mixture models in practice. In the case of mixture models, local maxima often in