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A New Coefficient of Correlation

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  • 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
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    Cited by:

    1. Zhang, Qingyang, 2023. "On the asymptotic null distribution of the symmetrized Chatterjee’s correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 194(C).
    2. Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.
    3. 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.
    4. 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.
    5. 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).
    6. Junlong Feng & Sokbae Lee, 2023. "Individual Welfare Analysis: Random Quasilinear Utility, Independence, and Confidence Bounds," Papers 2304.01921, arXiv.org, revised Jun 2024.
    7. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.
    8. 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.
    9. Juan C. King & Roberto Dale & Jos'e M. Amig'o, 2024. "Blockchain Metrics and Indicators in Cryptocurrency Trading," Papers 2403.00770, arXiv.org.
    10. King, Juan C. & Dale, Roberto & Amigó, José M., 2024. "Blockchain metrics and indicators in cryptocurrency trading," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    11. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.
    12. 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.
    13. 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.
    14. 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.
    15. Borgonovo, Emanuele & Ghidini, Valentina & Hahn, Roman & Plischke, Elmar, 2023. "Explaining classifiers with measures of statistical association," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    16. 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.
    17. Tobias Fissler & Marc-Oliver Pohle, 2023. "Generalised Covariances and Correlations," Papers 2307.03594, arXiv.org, revised Sep 2023.

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