Dependence in elliptical partial correlation graphs

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• dc.contributor.author Rossell Ribera, David
• dc.contributor.author Zwiernik, Piotr
• dc.date.accessioned 2023-06-16T06:18:44Z
• dc.date.available 2023-06-16T06:18:44Z
• dc.date.issued 2021
• dc.description.abstract The Gaussian model equips strong properties that facilitate studying and interpreting graphical models. Specifically it reduces conditional independence and the study of positive association to determining partial correlations and their signs. When Gaussianity does not hold partial correlation graphs are a useful relaxation of graphical models, but it is not clear what information they contain (besides the obvious lack of linear association). We study elliptical and transelliptical distributions as middleground between the Gaussian and other families that are more flexible but either do not embed strong properties or do not lead to simple interpretation. We characterize the meaning of zero partial correlations in elliptical and elliptical copula models and show that they retain much of the dependence structure from the Gaussian case. Regarding positive dependence, we prove impossibility results to learn certain positive (trans)elliptical graphical models, including that an elliptical distribution that is multivariate totally positive of order two for all dimensions must be essentially Gaussian. We then show how to interpret positive partial correlations as a relaxation, and obtain important properties related to faithfulness and Simpson’s paradox. We illustrate the transelliptical model potential to study tail dependence in S&P500 data, and of positivity to improve regularized inference.
• dc.description.sponsorship DR and PZ were supported from the Spanish Government grants (RYC-2015-18544, RYC2017-22544, PGC2018-101643-B-I00), and Ayudas Fundación BBVA a Equipos de Investigación Cientifica 2017. DR was partially supported by NIH grant R01 CA158113-01 and Europa Excelencia EUR2020-112096.
• dc.format.mimetype application/pdf
• dc.identifier.citation Rossell D, Zwiernik P. Dependence in elliptical partial correlation graphs. Electron J Statist. 2021;15(2):4236-63. DOI: 10.1214/21-EJS1891
• dc.identifier.doi http://dx.doi.org/10.1214/21-EJS1891
• dc.identifier.issn 1935-7524
• dc.identifier.uri http://hdl.handle.net/10230/57194
• dc.language.iso eng
• dc.publisher Institute of Mathematical Statistics
• dc.publisher Bernoulli Society for Mathematical Statistics and Probabilit
• dc.relation.ispartof Electronic Journal of Statistics. 2021;15(2):4236-63.
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/RYC-2015-18544
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/RYC-2017-22544
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00
• dc.rights This publication is under a Creative Commons Attribution 4.0 International License.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Partial correlation graph
• dc.subject.keyword elliptical distribution
• dc.subject.keyword transelliptical distribution
• dc.subject.keyword graphical models
• dc.subject.keyword multivariate total positivity
• dc.title Dependence in elliptical partial correlation graphs
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion