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A generalization of Hoeffding's lemma, and a new class of covariance inequalities

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  • Beare, Brendan K.

Abstract

We generalize Hoeffding's lemma to apply to covariances between functions of several random variables. Our generalization leads to a new class of covariance inequalities involving the Vitali or Hardy-Krause variation. These inequalities are relevant to the study of weakly dependent processes.

Suggested Citation

  • Beare, Brendan K., 2009. "A generalization of Hoeffding's lemma, and a new class of covariance inequalities," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 637-642, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:637-642
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    References listed on IDEAS

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    1. Brendan K. Beare, 2007. "A New Mixing Condition," Economics Series Working Papers 348, University of Oxford, Department of Economics.
    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. Christiane Lemieux, 2018. "Negative Dependence, Scrambled Nets, and Variance Bounds," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 228-251, February.
    2. Guo, Xu & Li, Jingyuan & Liu, Dongri & Wang, Jianli, 2016. "Preserving the Rothschild–Stiglitz type of increasing risk with background risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 144-149.
    3. 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.
    4. Xiaojun Song & Zhenting Sun, 2023. "Almost Dominance: Inference and Application," Papers 2312.02288, arXiv.org.
    5. Brendan K. Beare, 2007. "A New Mixing Condition," Economics Series Working Papers 348, University of Oxford, Department of Economics.
    6. Garg, Mansi & Dewan, Isha, 2015. "On asymptotic behavior of U-statistics for associated random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 209-220.

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