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A Basic Treatment of the Distance Covariance

Author

Listed:
  • Dominic Edelmann

    (German Cancer Research Center)

  • Tobias Terzer

    (German Cancer Research Center)

  • Donald Richards

    (Pennsylvania State University)

Abstract

The distance covariance of Székely et al. (Ann. Statist., 35, 2769–2794 2007, 2009), a powerful measure of dependence between sets of multivariate random variables, has the crucial feature that it equals zero if and only if the sets are mutually independent. Hence the distance covariance can be applied to multivariate data to detect arbitrary types of non-linear associations between sets of variables. We provide in this article a basic, albeit rigorous, introductory treatment of the distance covariance. Our investigations yield an approach that can be used as the foundation for presentation of this important and timely topic even in advanced undergraduate- or junior graduate-level courses on mathematical statistics.

Suggested Citation

  • Dominic Edelmann & Tobias Terzer & Donald Richards, 2021. "A Basic Treatment of the Distance Covariance," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 12-25, May.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-021-00248-z
    DOI: 10.1007/s13571-021-00248-z
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    References listed on IDEAS

    as
    1. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2015. "A generalization of an integral arising in the theory of distance correlation," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 116-119.
    2. Zhou Zhou, 2012. "Measuring nonlinear dependence in time‐series, a distance correlation approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 438-457, May.
    3. Dominic Edelmann & Konstantinos Fokianos & Maria Pitsillou, 2019. "An Updated Literature Review of Distance Correlation and Its Applications to Time Series," International Statistical Review, International Statistical Institute, vol. 87(2), pages 237-262, August.
    4. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
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