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Compatible matrices of Spearman’s rank correlation. (English) Zbl 1453.60038

Summary: In this paper, we provide a negative answer to a long-standing open problem on the compatibility of Spearman’s rho matrices. Following an equivalence of Spearman’s rho matrices and linear correlation matrices for dimensions up to 9 in the literature, we show non-equivalence for dimensions 12 or higher. In particular, we connect this problem with the existence of a random vector under some linear projection restrictions in two characterization results.

MSC:

60E05 Probability distributions: general theory
62H20 Measures of association (correlation, canonical correlation, etc.)

Software:

QRM; CopulaModel
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References:

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