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Adapted Chatterjee correlation coefficient

Author

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  • Wang, Ya
  • Fang, Linjiajie
  • Jing, Bingyi

Abstract

The need to accurately quantify dependence between random variables is a growing concern across various academic disciplines. Current correlation coefficients are typically intended for one of two purposes: testing independence or measuring relationship strength. Despite some attempts to address both aspects, the performance of these measures is still easily affected by oscillation and local noise. To address these limitations, we propose a new coefficient of correlation called the Adapted Chatterjee Correlation Coefficient (AC3). AC3 is designed to accurately identify both independence and functional dependence between variables, even in the presence of noise. We establish the consistency and asymptotic theories of (AC3). Additionally, we present a novel method, called Iterative Signal Detection Procedure (ISDP), for local signal identification. Our numerical studies and real data application demonstrate that AC3 outperforms state-of-the-art methods in terms of general performance and detecting local signals.

Suggested Citation

  • Wang, Ya & Fang, Linjiajie & Jing, Bingyi, 2024. "Adapted Chatterjee correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:stapro:v:215:y:2024:i:c:s0167715224002104
    DOI: 10.1016/j.spl.2024.110241
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    References listed on IDEAS

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    1. Holger Dette & Karl F. Siburg & Pavel A. Stoimenov, 2013. "A Copula-Based Non-parametric Measure of Regression Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 21-41, March.
    2. Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
    3. Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.
    4. Ruth Heller & Yair Heller & Malka Gorfine, 2013. "A consistent multivariate test of association based on ranks of distances," Biometrika, Biometrika Trust, vol. 100(2), pages 503-510.
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