On Hoeffding decomposition in \(L_{p}\)
type: Item
instance of: scholarly article
title: On Hoeffding decomposition in \(L_{p}\)
zbMATH Open document ID: 1271.60027
published in: Illinois Journal of Mathematics
publication date: 2013-01-04T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1336049990
review text: The Hoeffding decomposition for a \(U\)-statistic of order \(d\) expresses the statistic as a sum of canonical statistics of orders \(k \leq d\). The classical result assumes the statistic is based on random variables with finite variance. \textit{J. Bourgain} [Semin. Anal. Fonct. 1979--1980, Expose No.4 (1980; Zbl 0454.46020)] extended the decomposition to the case with finite \(p\)th moments, \(p > 1\). The author provides a new approach to the proof of this result, improved \(L_p\) bounds, as well as new Rosenthal-type moment inequalities for canonical \(U\)-statistics.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 6122091
zbMATH Keywords: Hoeffding decomposition
zbMATH Keywords: canonical \(U\)-statistics
zbMATH Keywords: Rosenthal inequalities
author: Stanislaw Kwapień
reviewed by: Neville Weber
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6122091