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Distance correlation coefficients for Lancaster distributions

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

Abstract

We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series representation for the distance covariance for these distributions. To illustrate the general theory, we apply the series representation to derive explicit expressions for the distance covariance and distance correlation coefficients for the bivariate normal distribution and its generalizations of Lancaster type, the multivariate normal distributions, and the bivariate gamma, Poisson, and negative binomial distributions which are of Lancaster type.

Suggested Citation

  • Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2017. "Distance correlation coefficients for Lancaster distributions," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 19-39.
    • Handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:19-39
    DOI: 10.1016/j.jmva.2016.10.012
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    References listed on IDEAS

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    1. 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.
    2. Angelo Koudou, 1998. "Lancaster bivariate probability distributions with Poisson, negative binomial and gamma margins," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 95-110, June.
    3. Székely, Gábor J. & Rizzo, Maria L., 2012. "On the uniqueness of distance covariance," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2278-2282.
    4. 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.
    5. 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.
    6. Withers, Christopher S. & Nadarajah, Saralees, 2010. "Expansions for the multivariate normal," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1311-1316, May.
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    Cited by:

    1. Edelmann, Dominic & Móri, Tamás F. & Székely, Gábor J., 2021. "On relationships between the Pearson and the distance correlation coefficients," Statistics & Probability Letters, Elsevier, vol. 169(C).

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