On normal approximations to \(U\)-statistics

DOI10.1214/09-AOP474zbMath1186.62025arXiv0903.3081OpenAlexW2016212914MaRDI QIDQ971937

Bing-Yi Jing, Wang Zhou, Vidmantas Bentkus

Publication date: 17 May 2010

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.3081

zbMATH Keywords

rate of convergencecentral limit theorem\(U\)-statisticsBerry-Esseen boundnormal approximationsself-normalizedStudentized \(U\)-statistics

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05)

Related Items (8)

Edgeworth expansions for network moments ⋮ Gaussian approximation of nonlinear statistics on the sphere ⋮ Rates of convergence in the central limit theorem for nonlinear statistics under relaxed moment conditions ⋮ The Berry-Esseen bound for identically distributed random variables by Stein method ⋮ Cramér's type results for some bootstrapped \(U\)-statistics ⋮ Weighted approximations for Studentized \(U\)-statistics ⋮ Two-Term Edgeworth Expansions for the Classes of U- and V-statistics ⋮ Quantum U-statistics

Cites Work

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• Normal approximation for nonlinear statistics using a concentration inequality approach
• A Berry-Esseen bound for symmetric statistics
• Approximation of Nondegenerate U-Statistics
• Lyapunov-Type Bounds for U-Statistics
• A Class of Statistics with Asymptotically Normal Distribution

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