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Gaussian approximations for high-dimensional non-degenerate U-statistics via exchangeable pairs

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  • Cheng, Guanghui
  • Liu, Zhi
  • Peng, Liuhua

Abstract

In this paper, we obtain a non-asymptotic bound for Gaussian approximations for centered high-dimensional non-degenerate U-statistics over the class of hyperrectangles via exchangeable pairs and Stein’s method. We improve the upper bound of the convergence rate from n−1/6 in Chen (2018) to n−1/4 up to a polynomial factor of logd under the same conditions, where n is the sample size and d is the dimension of the U-statistic. Convergence to zero of the bound requires logd=o(n1/7) in Chen (2018), this requirement on d is weaken in this paper by allowing logd=o(n1/5).

Suggested Citation

  • Cheng, Guanghui & Liu, Zhi & Peng, Liuhua, 2022. "Gaussian approximations for high-dimensional non-degenerate U-statistics via exchangeable pairs," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s0167715221002571
    DOI: 10.1016/j.spl.2021.109295
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2019. "Improved Central Limit Theorem and bootstrap approximations in high dimensions," Papers 1912.10529, arXiv.org, revised May 2022.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
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