Almost sure limit theorems for \(U\)-statistics
type: Item
instance of: scholarly article
title: Almost sure limit theorems for \(U\)-statistics
zbMATH Open document ID: 1068.60030
author: Hajo Holzmann
author: Susanne Koch
author: Aleksey Min
published in: Statistics \& Probability Letters
publication date: 2005-04-21T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 2160021
zbMATH Keywords: functional limit theorem
zbMATH Keywords: stable distributions
reviewed by: Neville Weber
MaRDI profile type: Publication
full work available at URL: j.spl.2004.06.019
OpenAlex ID: W1978254895
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DOI: 10.1016/J.SPL.2004.06.019
description: scientific article; zbMATH DE number 2160021