A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweights: Application to robust clustering

Wraith, Darren; Forbes, Florence

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

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Type

Article accepté pour publication ou publié

External document link

http://hal.inria.fr/hal-00823451

Date

2014

Journal name

Statistics and Computing

Volume

Number

Publisher

Springer

Pages

971-984

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 / Keywords

Outlier detection; Multivariate generalized t -distribution; Gaussian scale mixture; EM algorithm; Covariance matrix decomposition