Best-possible bounds on the set of copulas with a given value of Spearman's footrule
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2022Resumen
In this paper we find pointwise best-possible bounds on the set of copulas with a given value of the Spearman’s footrule co-efficient. We show that the lower bound is always a copula but, unlike the bounds on sets of copulas with a given value of other measures, such as Kendall’s tau, Spearman’s rho and Blonqvist’s beta, the upper bound can be a copula or a proper quasi-copula. We characterised both of these cases.
Palabra/s clave
Bounds
Copula
Lipschitz condition
Quasi-copula
Spearman’s footrule