Weakly Homoscedastic Constraints for Mixtures of t-Distributions

In this paper we introduce the concept of weak homoscedasticity for covariance matrices of the component densities, in the framework of constrained formulations of the maximum likelihood estimation for mixture models. Further, we give a test for assessing weak homoscedasticity in two sample data. Based on such approach, we present how to implement a constrained EMalgorithm for mixtures of t-distributions. The proposal is illustrated on the ground of numerical experiments which show its usefulness in data modeling and classification.