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The centred parameterization and related quantities of the skew-t distribution

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  • Arellano-Valle, Reinaldo B.
  • Azzalini, Adelchi

Abstract

The skew-t family, in its univariate and multivariate versions, is a parametric family of probability distributions which is currently under intense investigation because of several appealing properties. The present paper addresses the question of the choice of its parameterization, and more generally of the selection of quantities of interest associated to this distribution.

Suggested Citation

  • Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2013. "The centred parameterization and related quantities of the skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 73-90.
    • Handle: RePEc:eee:jmvana:v:113:y:2013:i:c:p:73-90
    DOI: 10.1016/j.jmva.2011.05.016
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    References listed on IDEAS

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    1. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    2. Christophe Ley & Davy Paindaveine, 2010. "On Fisher information matrices and profile log-likelihood functions in generalized skew-elliptical models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 235-250.
    3. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    4. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    5. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "Moments of random vectors with skew t distribution and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 417-423, July.
    6. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2008. "The centred parametrization for the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1362-1382, August.
    7. Reinaldo B. Arellano-Valle, 2010. "On the information matrix of the multivariate skew-t model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 371-386.
    8. 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.
    9. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    10. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    11. Monica Chiogna, 2005. "A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 331-341, December.
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    2. Bevilacqua, Moreno & Caamaño-Carrillo, Christian & Porcu, Emilio, 2022. "Unifying compactly supported and Matérn covariance functions in spatial statistics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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