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

Guanghui Cheng, Zhi Liu and Liuhua Peng

Statistics & Probability Letters, 2022, vol. 182, issue C

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).

Keywords: Exchangeable pairs; Gaussian approximation; High-dimensional; Non-asymptotic bound; Stein’s method; U-statistics (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109295

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