IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v116y2021i536p2009-2022.html
   My bibliography  Save this article

A New Coefficient of Correlation

Author

Listed:
  • Sourav Chatterjee

Abstract

Abstract–Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson’s correlation or Spearman’s correlation, and yet (b) consistently estimates some simple and interpretable measure of the degree of dependence between the variables, which is 0 if and only if the variables are independent and 1 if and only if one is a measurable function of the other, and (c) has a simple asymptotic theory under the hypothesis of independence, like the classical coefficients? This article answers this question in the affirmative, by producing such a coefficient. No assumptions are needed on the distributions of the variables. There are several coefficients in the literature that converge to 0 if and only if the variables are independent, but none that satisfy any of the other properties mentioned above. Supplementary materials for this article are available online.

Suggested Citation

  • Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:536:p:2009-2022
    DOI: 10.1080/01621459.2020.1758115
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2020.1758115
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2020.1758115?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 search for a different version of it.

    Citations

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


    Cited by:

    1. H Shi & M Drton & F Han, 2022. "On the power of Chatterjee’s rank correlation [Adaptive test of independence based on HSIC measures]," Biometrika, Biometrika Trust, vol. 109(2), pages 317-333.
    2. Jin Han & Liang Yang, 2024. "Sentence Embedding Generation Framework Based on Kullback–Leibler Divergence Optimization and RoBERTa Knowledge Distillation," Mathematics, MDPI, vol. 12(24), pages 1-21, December.
    3. Juan C. King & Roberto Dale & Jos'e M. Amig'o, 2024. "Blockchain Metrics and Indicators in Cryptocurrency Trading," Papers 2403.00770, arXiv.org.
    4. Karch, Julian D. & Perez-Alonso, Andres F. & Bergsma, Wicher P., 2024. "Beyond Pearson’s correlation: modern nonparametric independence tests for psychological research," LSE Research Online Documents on Economics 124587, London School of Economics and Political Science, LSE Library.
    5. Zhang, Qingyang, 2023. "On the asymptotic null distribution of the symmetrized Chatterjee’s correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 194(C).
    6. Borgonovo, Emanuele & Plischke, Elmar & Rabitti, Giovanni, 2024. "The many Shapley values for explainable artificial intelligence: A sensitivity analysis perspective," European Journal of Operational Research, Elsevier, vol. 318(3), pages 911-926.
    7. Junlong Feng & Sokbae Lee, 2023. "Individual Welfare Analysis: Random Quasilinear Utility, Independence, and Confidence Bounds," Papers 2304.01921, arXiv.org, revised Nov 2024.
    8. Ziming Lin & Fang Han, 2024. "On the consistency of bootstrap for matching estimators," Papers 2410.23525, arXiv.org, revised Nov 2024.
    9. Qingyang Zhang, 2024. "Asymptotic expected sensitivity function and its applications to measures of monotone association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 877-896, October.
    10. Borgonovo, Emanuele & Ghidini, Valentina & Hahn, Roman & Plischke, Elmar, 2023. "Explaining classifiers with measures of statistical association," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    11. Linyu Cao & Ruili Sun & Tiefeng Ma & Conan Liu, 2023. "On Asymmetric Correlations and Their Applications in Financial Markets," JRFM, MDPI, vol. 16(3), pages 1-18, March.
    12. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.
    13. Almanza Junco, Carlos Alberto & Parra Acosta, Yenny Katherine & Sabogal Salamanca, Mauricio, 2024. "Model of innovation in agriculture 4.0 processes in the department of Cundinamarca, Colombia," Revista Tendencias, Universidad de Narino, vol. 25(2), pages 86-112, July.
    14. King, Juan C. & Dale, Roberto & Amigó, José M., 2024. "Blockchain metrics and indicators in cryptocurrency trading," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    15. Tobias Fissler & Marc-Oliver Pohle, 2023. "Generalised Covariances and Correlations," Papers 2307.03594, arXiv.org, revised Sep 2023.
    16. Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.
    17. Borgonovo, Emanuele & Clemente, Gian Paolo & Rabitti, Giovanni, 2024. "Why insurance regulators need to require sensitivity settings of internal models for their approval," Finance Research Letters, Elsevier, vol. 60(C).
    18. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.
    19. Zhaoyang Li & Yuehan Yang, 2024. "A semi-orthogonal nonnegative matrix tri-factorization algorithm for overlapping community detection," Statistical Papers, Springer, vol. 65(6), pages 3601-3619, August.
    20. Abdol Rassoul Zarei & Marzieh Mokarram & Mohammad Reza Mahmoudi, 2023. "Comparison of the capability of the Meteorological and Remote Sensing Drought Indices," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(2), pages 769-796, January.

    More about this item

    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:taf:jnlasa:v:116:y:2021:i:536:p:2009-2022. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.