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.