On attainability of Kendall’s tau matrices and concordance signatures

Methods are developed for checking and completing systems of bivariate multivariate Kendall’s tau concordance measures in applications where only partial information about dependencies between variables is available. The concept a signature continuous distribution introduced; this the vector probabilities margins all orders. It shown that every attainable equal to unique mixture extremal copulas, copulas with correlation matrices consisting exclusively 1’s −1’s. A method estimating an from data derived correspond using standard estimates absence ties. set Kendall rank distributions proved be identical convex combinations matrices, known as cut polytope. methodology testing attainability signatures linear optimization analysis provided. elliptical yield strict subset well matrices; Student t copula seen converge, degrees freedom tend zero, sharing its have same matrix. characterization equiconcordant given.