A note on Edgeworth expansions for \(U\)-statistics under minimal conditions
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 \(\lim_{t\to \infty} t^{5/3}P(|h(X_1, X_2)| > t)\to 0\).
scientific article; zbMATH DE number 5076509