Testing the Number of Components in Finite Mixture Models
AbstractThis 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.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-867.
Length: 38 pages
Date of creation: Nov 2012
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Other versions of this item:
- 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.
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