Vector Copulas and Vector Sklar Theorem

Speaker: Yanqin Fan

Date: Sat, Jan 30, 2021

Location: Zoom

Conference: PIHOT kick-off event

Subject: Mathematics

Class: Scientific

CRG: Pacific Interdisciplinary Hub on Optimal Transport (2021-2024)


This talk introduces vector copulas and establishes a vector version of Sklar’s theorem. The latter provides a theoretical justification for the use of vector copulas to characterize nonlinear or rank dependence between a finite number of random vectors (robust to within vector dependence), and to construct multivariate distributions with any given non-overlapping multivariate marginals. We construct Elliptical, Archimedean, and Kendall families of vector copulas and present algorithms to generate data from them. We introduce a concordance ordering for two random vectors with given within-dependence structures and generalize Spearman’s rho to random vectors. Finally, we construct empirical vector copulas and show their consistency under mild conditions.

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