On the Exact Region Determined by Kendall's τ and Spearman's ρ
On the Exact Region Determined by Kendall's τ and Spearman's ρ
Using properties of shuffles of copulas and tools from combinatorics we solve the open question about the exact region $\Omega$ determined by all possible values of Kendall's $\tau$ and Spearman's $\rho$. In particular, we prove that the well-known inequality established by Durbin and Stuart in 1951 is only sharp on …