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Multivariate copulas with hairpin support

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Volume
130
Identifiers
DOI: 10.1016/j.jmva.2014.06.009
Keywords
  • Copula
  • Stochastic Measure
  • Hairpin Support
  • Extreme Points
Disciplines
  • Mathematics

Abstract

Abstract The notion of a two-dimensional hairpin allows for two different extensions to the general multivariate setting—that of a sub-hairpin and that of a super-hairpin. We study existence and uniqueness of ρ-dimensional copulas whose support is contained in a sub- (or super-) hairpin and extend various results about doubly stochastic measures to the general multivariate setting. In particular, we show that each copula with hairpin support is necessarily an extreme point of the convex set of all ρ-dimensional copulas. Additionally, we calculate the corresponding Markov kernels and, using a simple analytic expression for sub- (or super-) hairpin copulas, analyze the strong interrelation with copulas having a fixed diagonal section. Several examples and graphics illustrate both the chosen approach and the main results.

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