We determine the upper and lower bounds for possible values of Kendall's tau of a bivariate copula given that the value of its Spearman's footrule or Gini's gamma is known, and show that these bounds are always attained.
Published in Annals of the Institute of Statistical Mathematics
In this paper we define multivariate versions of the medial correlation coefficient and the rank correlation coefficient Spearman’s footrule in terms of copulas. We also present corresponding results for the sample statistic and provide a comparison of lower bounds among different measures of multivariate association.
