Wang, Qiying; Weber, Neville C. Exact convergence rate and leading term in the central limit theorem for \(U\)-statistics. (English) Zbl 1109.62013 Stat. Sin. 16, No. 4, 1409-1422 (2006). Summary: The leading term in the normal approximation to the distribution of \(U\)-statistics of degree 2 is derived. This result is applied to establish the exact rate of convergence in the Central Limit Theorem for \(U\)-statistics and to obtain the one-term Edgeworth expansion for the distribution function. Analogous results for more general \(U\)-type statistics are also considered. Cited in 1 Document MSC: 62E20 Asymptotic distribution theory in statistics 60F05 Central limit and other weak theorems Keywords:Berry-Esséen theorem; characterisation of rate of convergence; optimal moments; nonlattice condition; \(L\)-statistics PDFBibTeX XMLCite \textit{Q. Wang} and \textit{N. C. Weber}, Stat. Sin. 16, No. 4, 1409--1422 (2006; Zbl 1109.62013)