Almost sure limit theorems for \(U\)-statistics
\textit{I. Berkes} and \textit{E. Csaki} [Stochastic Processes Appl. 94, 105--134 (2001; Zbl 1053.60022)] obtained a general result for almost sure limit theorems (ASLT) and applied it to various statistics including \(U\)-statistics. The authors show that the ASLT for \(U\)-statistics holds under the same moment conditions as \textit{V. S. Koroljuk} and \textit{Y. V. Borovskikh} established for weak convergence [``Theory of \(U\)-statistics'' (1994; Zbl 0785.60015)]. Extensions to functional limit theorems are obtained. Further, for non-degenerate \(U\)-statistics, conditions are provided for the ASLT corresponding to convergence to stable limit distributions.
scientific article; zbMATH DE number 2160021
scientific article