On the exact region determined by Kendall's τ and Spearman's ρ

By M. Schreyer, R. Paulin, Wolfgang Trutschnig. 2015

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Using properties of shuffles of copulas and tools from combinatorics we solve the open question about the exact region Ω determined by all possible values of Kendall's τ and Spearman's ρ. In particular, we prove that the well‐known inequality established by Durbin and Stuart in 1951 is not sharp outside a countable set, give a simple analytic characterization of Ω in terms of a continuous, strictly increasing piecewise concave function and show that Ω is compact and simply connected, but not convex. The results also show that for each (x,y) ∈ Ω there are mutually completely dependent random variables X and Y whose τ‐ and ρ‐values coincide with x and y respectively.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a69595c105e52ce5ab32a0d58b69d042d4ebf03c

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In Statistics and Probability

Citations in the corpus

Variations in sustainable development goal interactions: Population, regional, and income disaggregation (2020, background): “The statistical inference of the interre21 lation between both correlation coefficients complies the defined calculations −1 ≤ 3τ − 2rs ≤ 1 (Daniels, 1944) and 22 yields the set Ω (Schreyer et al., 2017).”