This talk is concerned with an important issue in finite mixture modeling, namely the selection of the number of mixing components. A new penalized likelihood method is proposed for finite multivariate Gaussian mixture models, and it is shown to be statistically 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 real data analysis are presented to illustrate the performance of the proposed method.
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