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On the construction of minimum information bivariate copula families

Lookup NU author(s): Professor Kevin Wilson

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

Abstract

Copulas have become very popular as modelling tools in probability applications. Given a finite number of expectation constraints for functions defined on the unit square, the minimum information copula is that copula which has minimum information (Kullback–Leibler divergence) from the uniform copula. This can be considered the most “independent” copula satisfying the constraints. We demonstrate the existence and uniqueness of such copulas, rigorously establish the relation with discrete approximations, and prove an unexpected relationship between constraint expectation values and the copula density formula.

Publication metadata

Author(s): Bedford T, Wilson KJ

Publication type: Article

Publication status: Published

Journal: Annals of the Institute of Statistical Mathematics

Year: 2014

Volume: 66

Issue: 4

Pages: 703-723

Print publication date: 01/08/2014

Online publication date: 20/08/2013

Acceptance date: 25/06/2013

Date deposited: 23/09/2015

ISSN (print): 0020-3157

ISSN (electronic): 1572-9052

Publisher: Springer

URL: http://dx.doi.org/10.1007/s10463-013-0422-0

DOI: 10.1007/s10463-013-0422-0

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