A note on Edgeworth expansions for \(U\)-statistics under minimal conditions
type: Item
instance of: scholarly article
title: A note on Edgeworth expansions for \(U\)-statistics under minimal conditions
zbMATH Open document ID: 1100.62018
author: Wang Zhou
author: Bing-Yi Jing
published in: Lithuanian Mathematical Journal
publication date: 2006-11-28T00:00:00Z
review text: A one-term Edgeworth expansion for U-statistics with kernel \(h(x,y)\) was derived by \textit{B.-Y. Jing} and \textit{Q. Wang} [Ann. Stat. 31, No.~4, 1376--1391 (2003; Zbl 1052.62018] under optimal moment conditions. We show that one of the optimal moment conditions \(E| h(X 1, X_2|^{5/3} < \infty\); can be weakened to \(\lim_{t\to \infty} t^{5/3}P(|h(X_1, X_2)| > t)\to 0\).
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 5076509
zbMATH Keywords: optimal moments
zbMATH Keywords: nonlattice condition
MaRDI profile type: Publication
full work available at URL: s10986-005-0036-1
OpenAlex ID: W2055177238
cites work: Q4889006
cites work: Lower estimates of the convergence rate for \(U\)-statistics
cites work: Edgeworth expansion for \(U\)-statistics under minimal conditions.
DOI: 10.1007/S10986-005-0036-1
description: scientific article; zbMATH DE number 5076509