Edgeworth expansion for \(U\)-statistics under minimal conditions.

DOI10.1214/aos/1059655916zbMath1052.62018OpenAlexW1982244959MaRDI QIDQ1434017

Qiying Wang, Bing-Yi Jing

Publication date: 1 July 2004

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

Full work available at URL: https://projecteuclid.org/euclid.aos/1059655916

zbMATH Keywords

\(U\)-statisticsEdgeworth expansionnonlattice conditionoptimal moments

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Strong limit theorems (60F15)

Related Items (8)

Edgeworth expansions for network moments ⋮ A note on Edgeworth expansions for \(U\)-statistics under minimal conditions ⋮ On the Edgeworth expansion for elementary polynomials based on trimmed samples ⋮ On normal approximations to \(U\)-statistics ⋮ Two-Term Edgeworth Expansions for the Classes of U- and V-statistics ⋮ SMALL BANDWIDTH ASYMPTOTICS FOR DENSITY-WEIGHTED AVERAGE DERIVATIVES ⋮ On the bootstrap for Moran's \(I\) test for spatial dependence ⋮ Edgeworth expansion for the kernel quantile estimator

Cites Work

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• A Berry-Esseen bound for functions of independent random variables
• Convergence rates for U-statistics and related statistics
• On the Berry-Esseen theorem for U-statistics
• The Berry-Esseen theorem for U-statistics
• The Edgeworth expansion for U-statistics of degree two
• Edgeworth expansions in nonparametric statistics
• Lower estimates of the convergence rate for \(U\)-statistics
• Optimal rates of convergence in the CLT for quadratic forms
• A Class of Statistics with Asymptotically Normal Distribution

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