Vector Copulas and Vector Sklar Theorem


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.

2021-01-30 11:00 AM PST
Yanqin Fan (University of Washington (Econ))
Online (zoom)
Pacific Institute for the Mathematical Sciences

This event is part of the Pacific Interdisciplinary Hub on Optimal Transport (PIHOT) which is a collaborative research group (CRG) of the Pacific Institute for the Mathematical Sciences (PIMS).