Compatible matrices of Spearman’s rank correlation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2019Embargo end date: 01 Oct 2018 English Publisher:Elsevier BVJournal:Statistics & Probability Letters, volume 151, pages 67-72 (issn: 0167-7152,

Copyright policy )Funded by:NSERC | unidentified

Authors: Bin Wang; Ruodu Wang; Yuming Wang;

doi: 10.1016/j.spl.2019.03.015 , 10.48550/arxiv.1810.03477

arXiv: 1810.03477

Compatible matrices of Spearman’s rank correlation

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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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Chinese Academy of Sciences (中国科学院)
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Keywords

FOS: Computer and information sciences, Measures of association (correlation, canonical correlation, etc.), Mathematics - Statistics Theory, Statistics Theory (math.ST), compatibility, rank correlation matrix, risk management, Statistics - Applications, FOS: Mathematics, copula, Probability distributions: general theory, Applications (stat.AP), Spearman's rho

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