Testing the Number of Components in Normal Mixture Regression Models

Abstract

Testing the number of components in finite normal mixture models is a long-standing challenge because of its nonregularity. This article studies likelihood-based testing of the number of components in normal mixture regression models with heteroscedastic components. We construct a likelihood-based test of the null hypothesis of m₀ components against the alternative hypothesis of m₀ + 1 components for any m₀. The null asymptotic distribution of the proposed modified EM test statistic is the maximum of m₀ random variables that can be easily simulated. The simulations show that the proposed test has very good finite sample size and power properties. Supplementary materials for this article are available online.

• Asymptotic distribution
• Likelihood ratio test
• Local MLE
• Modified EM test
• Normal mixture models
• Number of components

Additional information

Notes on contributors

Hiroyuki Kasahara

Hiroyuki Kasahara, Vancouver School of Economics, University of British Columbia, 997-1873 East Mall, Vancouver, BC V6T 1Z1, Canada (E-mail: [email protected]). Katsumi Shimotsu, Faculty of Economics, University of Tokyo, Tokyo 113-0033 (E-mail: [email protected]). The authors are grateful to the editor, the associated editor, and two anonymous referees whose comments greatly improved the article. This research is supported by the Natural Science and Engineering Research Council of Canada and JSPS Grant-in-Aid for Scientific Research (C) No. 26380267.

Katsumi Shimotsu

Hiroyuki Kasahara, Vancouver School of Economics, University of British Columbia, 997-1873 East Mall, Vancouver, BC V6T 1Z1, Canada (E-mail: [email protected]). Katsumi Shimotsu, Faculty of Economics, University of Tokyo, Tokyo 113-0033 (E-mail: [email protected]). The authors are grateful to the editor, the associated editor, and two anonymous referees whose comments greatly improved the article. This research is supported by the Natural Science and Engineering Research Council of Canada and JSPS Grant-in-Aid for Scientific Research (C) No. 26380267.