Constrained monotone EM algorithms for mixture of multivariate t-distributions

Mixtures of multivariate t-distributions provide a robust parametric extension to the fitting of data with respect to normal mixtures. In presence of some noise component, potential outliers or data with longer-than-normal tails, one way to broaden the model can be provided by considering $t$ distributions. In this framework, the degrees of freedom can act as a robustness parameter, tuning the heaviness of the tails, and down weighting the effect of the outliers on the parameters estimation. The aim of this paper is to extend to mixtures of multivariate elliptical distributions some theoretical results about the likelihood maximization on constrained parameter spaces. Further, a constrained monotone algorithm implementing maximum likelihood mixture decomposition of multivariate t-distributions is proposed, to achieve improved convergence capabilities and robustness. Monte Carlo numerical simulations and a real data study demonstrate the better performance of the algorithm, comparing it to earlier proposals