Invariant dependence structure under univariate truncation: the high-dimensional case

Abstract

In this paper, the class of all multivariate copulas that are invariant under univariate truncation is characterized.

Keywords:

• copula
• threshold copula
• univariate conditioning
• truncation of the first variable
• invariant copula

MSC 2010: :

• 62E10
• 60E05
• 60G70
• 62P05

Acknowledgements

The author acknowledges the support given by the Polish Ministry of Science and Higher Education, via the grant N N201 547838.

Notes

Sometimes in some special cases the conditional copula is called tail-dependence or threshold copula.

t ⁺ denotes the positive part of t, t ⁺=max(0, t).