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Functional generalizations of Hoeffding’s covariance lemma and a formula for Kendall’s tau

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  • Lo, Ambrose

Abstract

This note extends Hoeffding’s lemma from the covariance between two random variables to that between transformations of random variables, and provides clarification of several existing functional generalizations. In the same spirit as these results, an explicit integral formula of Kendall’s tau for general, possibly discontinuous random variables is also determined.

Suggested Citation

  • Lo, Ambrose, 2017. "Functional generalizations of Hoeffding’s covariance lemma and a formula for Kendall’s tau," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 218-226.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:218-226
    DOI: 10.1016/j.spl.2016.11.016
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    References listed on IDEAS

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    1. Cuadras, Carles M., 2015. "Contributions to the diagonal expansion of a bivariate copula with continuous extensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 28-44.
    2. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
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    Cited by:

    1. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    2. Liu, Yang, 2020. "A general treatment of alternative expectation formulae," Statistics & Probability Letters, Elsevier, vol. 166(C).
    3. Xiaojun Song & Zhenting Sun, 2023. "Almost Dominance: Inference and Application," Papers 2312.02288, arXiv.org.

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