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Geometry of discrete copulas
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2019 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 172, p. 162-169Article in journal (Refereed) Published
Abstract [en]

The space of discrete copulas admits a representation as a convex polytope, and this has been exploited in entropy-copula methods used in hydrology and climatology. In this paper, we focus on the class of component-wise convex copulas, i.e., ultramodular copulas, which describe the joint behavior of stochastically decreasing random vectors. We show that the family of ultramodular discrete copulas and its generalization to component-wise convex discrete quasi-copulas also admit representations as polytopes. In doing so, we draw connections to the Birkhoff polytope, the alternating sign matrix polytope, and their generalizations, thereby unifying and extending results on these polytopes from both the statistics and the discrete geometry literature.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 172, p. 162-169
Keywords [en]
Alternating sign matrix polytope, Convex optimization, Discrete (quasi-) copulas, Maximum entropy, Negative dependence, Stochastic decreasingness, Transportation polytope
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-251865DOI: 10.1016/j.jmva.2019.01.014ISI: 000470804600010Scopus ID: 2-s2.0-85062030416OAI: oai:DiVA.org:kth-251865DiVA, id: diva2:1318670
Note

QC 20190528

Available from: 2019-05-28 Created: 2019-05-28 Last updated: 2019-10-28Bibliographically approved

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Solus, Liam

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