Compatible Matrices of Spearman's Rank Correlation

2018/10/08 by Bin Wang, Ruodu Wang, Wang, Bin +3 · 1 citation
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #Random Matrices and Applications #graph theory and CDMA systems #math.ST #stat.AP #stat.TH

paper · pdf · doi:10.48550/arxiv.1810.03477

arxiv created 2019/04/03 · arxiv updated 2019/04/04

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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