{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/objective-priors-for-the-number-of-degrees-of","title":"Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula","arxiv_id":"1701.05638","date":"2017-01-19","proceeding":null,"authors":["Cristiano Villa","Francisco J. Rubio"],"abstract":"An objective Bayesian approach to estimate the number of degrees of freedom $(\\nu)$ 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 $\\nu$ 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. The 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.","url_abs":"https://arxiv.org/abs/1701.05638v4","url_pdf":"https://arxiv.org/pdf/1701.05638v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"objective-priors-for-the-number-of-degrees-of","repo_url":"https://github.com/CPJClare/Kullback-Leibler-divergence-multivariate-Student-s-t-versus-multivariate-normal","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"objective-priors-for-the-number-of-degrees-of","repo_url":"https://github.com/ConorCUIster/Kullback-Leibler-divergence-multivariate-Student-s-t-versus-multivariate-normal","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}