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Two matrix-variate distributions, both elliptical heavy-tailed generalization of the matrix-variate normal distribution, are introduced. They belong to the normal scale mixture family, and are respectively obtained by choosing a convenient shifted exponential or uniform as mixing distribution. Moreover, they have a closed-form for the probability density function that is characterized by only one additional parameter, with respect to the nested matrix-variate normal, governing the tail-weight. Both distributions are then used for model-based clustering via finite mixture models. The resulting mixtures, being able to handle data with atypical observations in a better way than the matrix-variate normal mixture, can avoid the disruption of the true underlying group structure. Different EM-based algorithms are implemented for parameter estimation and tested in terms of computational times and parameter recovery. Furthermore, these mixture models are fitted to simulated and real datasets, and their fitting and clustering performances are analyzed and compared to those obtained by other well-established competitors. [ABSTRACT FROM AUTHOR]

The proposed multiple scaled contaminated asymmetric Laplace (MSCAL) distribution is an extension of the multivariate asymmetric Laplace distribution to allow for a different excess kurtosis on each dimension and for more flexible shapes of the hyper-contours. These peculiarities are obtained by working on the principal component (PC) space. The structure of the MSCAL distribution has the further advantage of allowing for automatic PC-wise outlier detection – i.e., detection of outliers separately on each PC – when convenient constraints on the parameters are imposed. The MSCAL is fitted using a Monte Carlo expectation-maximization (MCEM) algorithm that uses a Monte Carlo method to estimate the orthogonal matrix of eigenvectors. A simulation study is used to assess the proposed MCEM in terms of computational efficiency and parameter recovery. In a real data application, the MSCAL is fitted to a real data set containing the anthropometric measurements of monozygotic/dizygotic twins. Both a skewed bivariate subset of the full data, perturbed by some outlying points, and the full data are considered. [ABSTRACT FROM AUTHOR]