Maximal Non-Exchangeability in Dimension d

Michael Harder; Ulrich Stadtmüller

doi:10.1016/j.jmva.2013.10.003

paper

Maximal Non-Exchangeability in Dimension d

arXiv:1311.5832 · doi:10.1016/j.jmva.2013.10.003

Abstract

We give the maximal distance between a copula and itself when the argument is permuted for arbitrary dimension, generalizing a result for dimension two by Nelsen (2007), Klement and Mesiar (2006). Furthermore, we establish a subset of $[0, 1]^{d}$ in which this bound might be attained. For each point in this subset we present a copula and a permutation, for which the distance in this point is maximal. In the process, we see that this subset depends on the dimension being even or odd.

12 pages, no figures