Title: Compatibility and attainability of matrices of correlation-based measures of concordance
Authors: Takaaki Koike - University of Waterloo (Canada) [presenting]
Marius Hofert - University of Waterloo (Canada)
Abstract: Measures of concordance have been widely used to summarize non-linear dependence among random variables, which Pearson's correlation coefficient cannot capture. However, popular measures of concordance, such as Spearman's rho and Blomqvist's beta, appear as classical correlations of transformed random variables. We characterize a whole class of such concordance measures arising from correlations of transformed random variables, which includes Spearman's rho, Blomqvist's beta and van der Waerden's coefficient as special cases. Compatibility and attainability of square matrices with entries given by such measures are studied, that is, whether a given square matrix can be realized as a matrix of such pairwise measures of concordance of some random vector, and how such a random vector can be constructed.