A remark on strong law of large numbers for weighted \(U\)-statistics
type: Item
instance of: scholarly article
title: A remark on strong law of large numbers for weighted \(U\)-statistics
zbMATH Open document ID: 1304.60038
author: Hyung-Tae Ha
author: Mei-Ling Huang
author: Deli Li
publication date: 2014-09-11T00:00:00Z
review text: This paper establishes a strong law of large numbers for weighted \(U\)-statistics with kernel function of degree \(m\) based on independent and identically distributed random variables, provided that the weights are uniformly bounded. The result for the case \(m=1\) coincides with a result in [\textit{B. D. Choi} and \textit{S. H. Sung}, Stochastic Anal. Appl. 5, 365--377 (1987; Zbl 0633.60049)]. The proof presented in this paper utilizes a new general result on complete convergence of an array of real-valued random variables which is of independent interest.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 6342525
zbMATH Keywords: weighted \(U\)-statistics
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: complete convergence
reviewed by: Neville Weber
MaRDI profile type: Publication
full work available at URL: s10114-014-1601-5
OpenAlex ID: W1981290866
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DOI: 10.1007/S10114-014-1601-5
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6342525