A note on the ASCLT for triangular arrays of random variables with an extension to U-statistics
type: Item
instance of: scholarly article
title: A note on the ASCLT for triangular arrays of random variables with an extension to U-statistics
zbMATH Open document ID: 1266.60058
author: Yong Zhang
author: Xiao-Yun Yang
publication date: 2013-03-15T00:00:00Z
review text: Let \(\{X_{ki}\}\) be a triangular array of independent and identically distributed positive random variables with finite absolute moments of order \(p>2.\) The authors extend the results of \textit{K. Gonchigdanzan} and \textit{G. Rempala} [Appl. Math. Lett. 19, No. 2, 191--196 (2006; Zbl 1088.60021)] to obtain an almost sure central limit theorem for products \(\prod_{k=1}^n S_k/k\), where \(S_k = \sum_{i=1}^{k} X_{ki}.\) The result is then applied to obtain the corresponding result for products of non-degenerate \(U\)-statistics with positive kernels based on a triangular array of iid random variables. Related triangular array results can be found by \textit{Y. Miao} [J. Dyn. Syst. Geom. Theor. 7, No. 1, 49--60 (2009; Zbl 1180.60030)].
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 6145424
zbMATH Keywords: almost sure central limit theorem
zbMATH Keywords: products of sums
zbMATH Keywords: triangular arrays
zbMATH Keywords: \(U\)-statistics
reviewed by: Neville Weber
MaRDI profile type: Publication
full work available at URL: s10114-012-9241-0
OpenAlex ID: W87644257
cites work: Limit distributions for products of sums.
cites work: Asymptotics for products of sums and \(U\)-statistics
cites work: A note on asymptotic distribution of products of sums
cites work: Asymptotics for products of independent sums with an application to Wishart determinants
cites work: Asymptotics for sums of a function of normalized independent sums
cites work: An almost everywhere central limit theorem
cites work: On Strong Versions of the Central Limit Theorem
cites work: On almost sure max-limit theorems of complete and incomplete samples from stationary sequences
cites work: A note on the almost sure limit theorem for the product of partial sums
cites work: A note on the almost sure central limit theorem for weakly dependent random variables
cites work: Q5560061
cites work: A Class of Statistics with Asymptotically Normal Distribution
DOI: 10.1007/S10114-012-9241-0
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6145424