A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweights: Application to robust clustering
Wraith, Darren; Forbes, Florence (2014), A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweights: Application to robust clustering, Statistics and Computing, 24, 6, p. 971-984. http://dx.doi.org/10.1007/s11222-013-9414-4
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.inria.fr/hal-00823451
Journal nameStatistics and Computing
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Abstract (EN)We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and ttails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering example.
Subjects / KeywordsOutlier detection; Multivariate generalized t -distribution; Gaussian scale mixture; EM algorithm; Covariance matrix decomposition
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