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Compatible Matrices of Spearman's Rank Correlation

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arxiv 1810.03477 v3 pith:KR4W5Y6U submitted 2018-10-08 math.ST stat.APstat.TH

Compatible Matrices of Spearman's Rank Correlation

classification math.ST stat.APstat.TH
keywords matricesspearmancorrelationdimensionslinearproblemanswercharacterization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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