Compatible Matrices of Spearman's Rank Correlation

Bin Wang; Ruodu Wang; Yuming Wang

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arXiv · 1810.03477

Compatible Matrices of Spearman's Rank Correlation

Bin Wang·Ruodu Wang·Yuming Wang

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Abstract

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.

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Bin Wang, Ruodu Wang, Yuming Wang. 2018-10-08. Compatible Matrices of Spearman's Rank Correlation. https://arxiv.org/abs/1810.03477

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