On the exact region determined by Spearman’s ρ and Blest’s measure of rank correlation ν for bivariate extreme-value copulas

Abstract

Considering pairs of measures of association it has been of interest how much the values of one measure varies, fixing the value of the other one. Motivated by this fact, we establish sharp lower and upper bounds for the region determined by Spearman’s $\rho$ and Blest’s measure of rank correlation $\nu$ for bivariate extreme-value copulas (EVCs). Moreover, in the well-studied class of EVCs, exact regions for Spearman’s footrule $\varphi$/Blomqvist’s $\beta$ and Spearman’s $\rho$, Kendall’s $\tau$ or Blest’s symmetrised measure of rank correlation $\xi$ are provided. A performance analysis comparing rank-based estimators of $\rho$ and $\nu$ with estimators using that the sample is drawn from an extreme-value copula concludes this paper.