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Compatible matrices of Spearman’s rank correlation

Author

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  • Wang, Bin
  • Wang, Ruodu
  • Wang, Yuming

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.

Suggested Citation

  • Wang, Bin & Wang, Ruodu & Wang, Yuming, 2019. "Compatible matrices of Spearman’s rank correlation," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 67-72.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:67-72
    DOI: 10.1016/j.spl.2019.03.015
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    References listed on IDEAS

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    1. N. Rao Chaganty & Harry Joe, 2006. "Range of correlation matrices for dependent Bernoulli random variables," Biometrika, Biometrika Trust, vol. 93(1), pages 197-206, March.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
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    Cited by:

    1. McNeil, Alexander J. & Nešlehová, Johanna G. & Smith, Andrew D., 2022. "On attainability of Kendall’s tau matrices and concordance signatures," Journal of Multivariate Analysis, Elsevier, vol. 191(C).

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