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Compatibility and attainability of matrices of correlation-based measures of concordance. (arXiv:1810.07126v1 [math.ST])
来源于:arXiv
Necessary and sufficient conditions are derived under which concordance
measures arise from correlations of transformed ranks of random variables.
Compatibility and attainability of square matrices with entries given by such
measures are studied, that is, whether a given square matrix of such measures
of association can be realized for some random vector and how such a random
vector can be constructed. Special cases of this framework include (matrices of
pairwise) Spearman's rho, Blomqvist's beta and van der Waerden's coefficient.
For these specific measures, characterizations of sets of compatible matrices
are provided. Compatibility and attainability of block matrices and
hierarchical matrices are also studied. In particular, a subclass of attainable
block Spearman's rho matrices is proposed to compensate for the drawback that
Spearman's rho matrices are in general not attainable for dimensions larger
than four. Another result concerns a novel analytical form of the Cholesky
factor o 查看全文>>