Testing the Number of Components in Finite Mixture Models

Hiroyuki Kasahara and Katsumi Shimotsu
Additional contact information
Katsumi Shimotsu: Faculty of Economics, University of Tokyo

No CIRJE-F-867, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper considers likelihood-based testing of the null hypothesis of m0 components against the alternative of m 0+1 components in a finite mixture model. The number of components is an important parameter in the applications of finite mixture models. Still, testing the number of components has been a long-standing challenging problem because of its non-regularity. We develop a framework that facilitates the analysis of the likelihood function of finite mixture models and derive the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of m 0 components against the alternative of m 0+1 components. Furthermore, building on this framework, we propose a likelihood-based testing procedure of the number of components. The proposed test, extending the EM approach of Li, Chen and Marriott (2009), does not use a penalty term and is implementable even when the likelihood ratio test is difficult to implement because of non-regularity and computational complexity.

Pages: 38 pages
Date: 2012-11
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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http://www.cirje.e.u-tokyo.ac.jp/research/dp/2012/2012cf867.pdf (application/pdf)

Related works:
Working Paper: Testing the Number of Components in Finite Mixture Models (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2012cf867

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