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Statistica Sinica 27 (2017), 147-169

MODEL SELECTION FOR GAUSSIAN MIXTURE MODELS
Tao Huang, Heng Peng and Kun Zhang
Shanghai University of Finance and Economics, Hong Kong Baptist University and
Carnegie Mellon University & Max Planck Institute for Intelligent Systems

Abstract: This paper is concerned with an important issue in nite mixture modeling, the selection of the number of mixing components. A new penalized likelihood method is proposed for nite multivariate Gaussian mixture models, and it is shown to be consistent in determining the number of components. A modified EM algorithm is developed to simultaneously select the number of components and estimate the mixing probabilities and the unknown parameters of Gaussian distributions. Simulations and a data analysis are presented to illustrate the performance of the proposed method.

Key words and phrases: EM algorithm, Gaussian mixture models, model selection, penalized likelihood.

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