This paper is concerned with an important issue in finite mixture modelling,
the selection of the number of mixing components. We propose a new penalized
likelihood method for model selection of finite multivariate Gaussian mixture
models. The proposed method is shown to be statistically consistent in
determining of the number of components. A modified EM algorithm is developed
to simultaneously select the number of components and to estimate the mixing
weights, i.e. the mixing probabilities, and unknown parameters of Gaussian
distributions. Simulations and a real data analysis are presented to illustrate
the performance of the proposed method