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Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula

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  • Villa, Cristiano
  • Rubio, Francisco J.

Abstract

An objective Bayesian approach to estimate the number of degrees of freedom (ν) for the multivariate t distribution and for the t-copula, when the parameter is considered discrete, is proposed. Inference on this parameter has been problematic for the multivariate t and, for the absence of any method, for the t-copula. An objective criterion based on loss functions which allows to overcome the issue of defining objective probabilities directly is employed. The support of the prior for ν is truncated, which derives from the property of both the multivariate t and the t-copula of convergence to normality for a sufficiently large number of degrees of freedom. The performance of the priors is tested on simulated scenarios 11The R codes and the replication material are available as a supplementary material of the electronic version of the paper.and on real data: daily logarithmic returns of IBM and of the Center for Research in Security Prices Database.

Suggested Citation

  • Villa, Cristiano & Rubio, Francisco J., 2018. "Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 197-219.
    • Handle: RePEc:eee:csdana:v:124:y:2018:i:c:p:197-219
    DOI: 10.1016/j.csda.2018.03.010
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    References listed on IDEAS

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    Cited by:

    1. Wang, Sheng & Zimmerman, Dale L. & Breheny, Patrick, 2020. "Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).

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