A measure of total variability for the multivariate t distribution with applications to finance
Information Sciences: an International Journal
Robust mixture modelling using the t distribution
Statistics and Computing
Bayesian analysis of mixture modelling using the multivariate t distribution
Statistics and Computing
Constrained monotone EM algorithms for finite mixture of multivariate Gaussians
Computational Statistics & Data Analysis
The infinite Student's t-mixture for robust modeling
Signal Processing
Multivariate mixture modeling using skew-normal independent distributions
Computational Statistics & Data Analysis
Dimension reduction for model-based clustering via mixtures of multivariate $$t$$t-distributions
Advances in Data Analysis and Classification
A multivariate linear regression analysis using finite mixtures of t distributions
Computational Statistics & Data Analysis
Model-based clustering via linear cluster-weighted models
Computational Statistics & Data Analysis
Parsimonious skew mixture models for model-based clustering and classification
Computational Statistics & Data Analysis
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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 downweighting 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 illustrate the better performance of the algorithm, comparing it to earlier proposals.