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The orthogonal skew model: computationally efficient multivariate skew-normal and skew-t distributions with applications to model-based clustering

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  • Ryan P. Browne

    (University of Waterloo)

  • Jeffrey L. Andrews

    (University of British Columbia)

Abstract

We introduce a parameterization for the multivariate skew normal and skew-t distributions, which enforces an orthogonal structure on the skewness parameter. This approach provides substantial benefits in computational efficiency during parameter estimation, resulting in a model which strikes an excellent balance between flexibility and model-fitting feasibility. We illustrate this primarily through implementing the proposed distributions in a mixture model-based clustering framework. We compare to competing skew distributions via both simulated and real data analyses, reporting both computation time and model-fit metrics.

Suggested Citation

  • Ryan P. Browne & Jeffrey L. Andrews, 2024. "The orthogonal skew model: computationally efficient multivariate skew-normal and skew-t distributions with applications to model-based clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 752-785, September.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:3:d:10.1007_s11749-024-00920-2
    DOI: 10.1007/s11749-024-00920-2
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    References listed on IDEAS

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    1. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.
    2. Sharon Lee & Geoffrey McLachlan, 2013. "Model-based clustering and classification with non-normal mixture distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 427-454, November.
    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    4. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    5. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    6. R.B. Arellano-Valle & H. Bolfarine & V.H. Lachos, 2007. "Bayesian Inference for Skew-normal Linear Mixed Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(6), pages 663-682.
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