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A generalization of an integral arising in the theory of distance correlation

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  • Dueck, Johannes
  • Edelmann, Dominic
  • Richards, Donald

Abstract

We generalize an integral which arises in several areas in probability and statistics and which is at the core of the field of distance correlation, a concept developed by Székely et al. (2007) to measure dependence between random variables.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:116-119
    DOI: 10.1016/j.spl.2014.11.012
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    References listed on IDEAS

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    1. 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.
    2. Székely, Gábor J. & Rizzo, Maria L., 2013. "The distance correlation t-test of independence in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 193-213.
    3. Gabor J. Szekely & Maria L. Rizzo, 2005. "Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 151-183, September.
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    Cited by:

    1. Jentsch, Carsten & Leucht, Anne & Meyer, Marco & Beering, Carina, 2016. "Empirical characteristic functions-based estimation and distance correlation for locally stationary processes," Working Papers 16-15, University of Mannheim, Department of Economics.
    2. 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.
    3. Chu, Ba, 2023. "A distance-based test of independence between two multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    4. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2017. "Distance correlation coefficients for Lancaster distributions," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 19-39.

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