On the convergence of \(U\)-statistics with stable limit distribution
type: Item
instance of: scholarly article
title: On the convergence of \(U\)-statistics with stable limit distribution
zbMATH Open document ID: 0768.60023
author: Werner Wolf
author: Lothar Heinrich
published in: Journal of Multivariate Analysis
publication date: 1993-05-16T00:00:00Z
review text: Weak sufficient conditions are given to ensure the convergence of the distribution of suitably normalized \(U\)-statistics to an \(\alpha\)-stable distribution, \(1<\alpha\leq 2\). The proofs use Hoeffding's decomposition for \(U\)-statistics. For a subset of cases covered by the above result a rate of convergence is given which is of the same order as the rate obtained for similar stable limit results for sums of independent and identically distributed random variables.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 168715
zbMATH Keywords: slowly varying function
zbMATH Keywords: stable distribution
zbMATH Keywords: Hoeffding's decomposition for \(U\)-statistics
zbMATH Keywords: convergence of the distribution
reviewed by: Neville Weber
MaRDI profile type: Publication
full work available at URL: jmva.1993.1015
OpenAlex ID: W2025494179
DOI: 10.1006/JMVA.1993.1015
description: scientific article; zbMATH DE number 168715