IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v151y2019icp67-72.html

Compatible matrices of Spearman’s rank correlation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219300914
    Download Restriction: Full text may be restricted for ScienceDirect subscribers
    File URL: https://libkey.io/10.1016/j.spl.2019.03.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Koike, Takaaki & Lin, Liyuan & Wang, Ruodu, 2024. "Invariant correlation under marginal transforms," Journal of Multivariate Analysis, Elsevier, vol. 204(C).
    2. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    2. Masahiko Egami & Rusudan Kevkhishvili, 2020. "Time reversal and last passage time of diffusions with applications to credit risk management," Finance and Stochastics, Springer, vol. 24(3), pages 795-825, July.
    3. Pfeifer Dietmar & Mändle Andreas & Ragulina Olena, 2017. "New copulas based on general partitions-of-unity and their applications to risk management (part II)," Dependence Modeling, De Gruyter, vol. 5(1), pages 246-255, October.
    4. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    5. Ruodu Wang & Jingcheng Yu, 2026. "E-Backtesting Expected Shortfall without Value-at-Risk Forecasts under Time-series Models," Papers 2610.17681, arXiv.org.
    6. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2024. "On comprehensive families of copulas involving the three basic copulas and transformations thereof," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-36.
    7. Conlon, Thomas & Cotter, John & Ropotos, Ioannis, 2026. "Drivers of firm-level tail dependence: A machine learning approach," Journal of Economic Dynamics and Control, Elsevier, vol. 182(C).
    8. Jose Blanchet & Henry Lam & Yang Liu & Ruodu Wang, 2025. "Convolution Bounds on Quantile Aggregation," Operations Research, INFORMS, vol. 73(5), pages 2761-2781, September.
    9. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    10. Dimitris Bertsimas & Agni Orfanoudaki, 2021. "Algorithmic Insurance," Papers 2106.00839, arXiv.org, revised Mar 2026.
    11. Tim J. Boonen & Wing Fung Chong & Mario Ghossoub, 2024. "Pareto‐efficient risk sharing in centralized insurance markets with application to flood risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 91(2), pages 449-488, June.
    12. Fangda Liu & Tiantian Mao & Ruodu Wang & Linxiao Wei, 2022. "Inf-Convolution, Optimal Allocations, and Model Uncertainty for Tail Risk Measures," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 2494-2519, August.
    13. Claudia Ceci & Katia Colaneri & Rdiger Frey & Verena Kock, 2019. "Value adjustments and dynamic hedging of reinsurance counterparty risk," Papers 1909.04354, arXiv.org.
    14. Chen, Yuyu & Hu, Taizhong & Wang, Ruodu & Zou, Zhenfeng, 2025. "Diversification for infinite-mean Pareto models without risk aversion," European Journal of Operational Research, Elsevier, vol. 323(1), pages 341-350.
    15. Karlsson, Sune & Mazur, Stepan & Nguyen, Hoang, 2023. "Vector autoregression models with skewness and heavy tails," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    16. Peng Liu, 2025. "Risk Sharing with Lambda Value at Risk," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 313-333, February.
    17. Sundusit Saekow & Phisanu Chiawkhun & Woraphon Yamaka & Nawapon Nakharutai & Parkpoom Phetpradap, 2024. "Estimation of Contagion: Bayesian Model Averaging on Tail Dependence of Mixture Copula," Mathematics, MDPI, vol. 12(21), pages 1-23, October.
    18. Yuanying Guan & Zhanyi Jiao & Ruodu Wang, 2022. "A reverse ES (CVaR) optimization formula," Papers 2203.02599, arXiv.org, revised May 2023.
    19. Shahzad, Muhammad Faisal & Abdulai, Awudu, 2020. "Adaptation to extreme weather conditions and farm performance in rural Pakistan," Agricultural Systems, Elsevier, vol. 180(C).
    20. Aditri, 2026. "Efficiency versus Robustness under Tail Misspecification: Importance Sampling and Moment-Based VaR Bracketing," Papers 2601.09927, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:67-72. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.