Vector Copulas and Vector Sklar Theorem

Speaker
Yanqin Fan, University of Washington (Econ)
Date
2021-01-30 11:00 AM PST
Event
PIHOT kick-off event
Location
Online (zoom)
Registration
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Abstract

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.