Estimation and order selection for multivariate exponential power mixture models

Finite mixture model is a promising statistical model in investigating the heterogeneity of population. For multivariate non-Gaussian density estimation and approximation, in this paper, we consider to use multivariate exponential power mixture models. We propose the penalized-likelihood method with a generalized EM algorithm to estimate locations, scale matrices, shape parameters, and mixing probabilities. Order selection is achieved simultaneously. Properties of the estimated order have been derived. Although we mainly focus on the unconstrained scale matrix type in multivariate exponential power mixture models, three more parsimonious types of scale matrix have also been considered. Performance based on simulation and real data analysis implies the parsimony of the exponential power mixture models, and verifies the consistency of order selection.