Model-based clustering via new parsimonious mixtures of heavy-tailed distributions

Two families of parsimonious mixture models are introduced for model-based clustering. They are based on two multivariate distributions-the shifted exponential normal and the tail-inflated normal-recently introduced in the literature as heavy-tailed generalizations of the multivariate normal. Parsimony is attained by the eigen-decomposition of the component scale matrices, as well as by the imposition of a constraint on the tailedness parameters. Identifiability conditions are also provided. Two variants of the expectation-maximization algorithm are presented for maximum likelihood parameter estimation. Parameter recovery and clustering performance are investigated via a simulation study. Comparisons with the unconstrained mixture models are obtained as by-product. A further simulated analysis is conducted to assess how sensitive our and some well-established parsimonious competitors are to their own generative scheme. Lastly, our and the competing models are evaluated in terms of fitting and clustering on three real datasets.