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Generalized R-squared for detecting dependence

Author

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  • X. Wang
  • B. Jiang
  • J. S. Liu

Abstract

SUMMARY Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation coefficient is effective for capturing linear dependence, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their relationship. The G-squared statistic is almost identical to the square of the Pearson correlation coefficient, R-squared, for linear relationships with constant error variance, and has the intuitive meaning of the piecewise R-squared between the variables. It is particularly effective in handling nonlinearity and heteroscedastic errors. We propose two estimators of G-squared and show their consistency. Simulations demonstrate that G-squared estimators are among the most powerful test statistics compared with several state-of-the-art methods.

Suggested Citation

  • X. Wang & B. Jiang & J. S. Liu, 2017. "Generalized R-squared for detecting dependence," Biometrika, Biometrika Trust, vol. 104(1), pages 129-139.
  • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:129-139.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw071
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    Cited by:

    1. 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.
    2. L Weihs & M Drton & N Meinshausen, 2018. "Symmetric rank covariances: a generalized framework for nonparametric measures of dependence," Biometrika, Biometrika Trust, vol. 105(3), pages 547-562.
    3. Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.

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