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Hoeffding–Serfling Inequality for U-Statistics Without Replacement

Author

Listed:
  • Jianhang Ai

    (Czech Technical University in Prague)

  • Ondřej Kuželka

    (Czech Technical University in Prague)

  • Yuyi Wang

    (ETH Zurich)

Abstract

Concentration inequalities quantify random fluctuations of functions of random variables, typically by bounding the probability that such a function differs from its expected value by more than a certain amount. In this paper we study one particular concentration inequality, the Hoeffding–Serfling inequality for U-statistics of random variables sampled without replacement from a finite set and extend recent results of Bardenet and Maillard (Bernoulli 21(3):1361–1385, 2015) to cover the U-statistics setting.

Suggested Citation

  • Jianhang Ai & Ondřej Kuželka & Yuyi Wang, 2023. "Hoeffding–Serfling Inequality for U-Statistics Without Replacement," Journal of Theoretical Probability, Springer, vol. 36(1), pages 390-408, March.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:1:d:10.1007_s10959-022-01169-x
    DOI: 10.1007/s10959-022-01169-x
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    References listed on IDEAS

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    1. Arcones, Miguel A., 1995. "A Bernstein-type inequality for U-statistics and U-processes," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 239-247, February.
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