On the central limit theorem for \(U\)-statistics under absolute regularity
type: Item
instance of: scholarly article
title: On the central limit theorem for \(U\)-statistics under absolute regularity
zbMATH Open document ID: 0835.60017
DOI: 10.1016/0167-7152(94)00179-C
author: Miguel A. Arcones
published in: Statistics \& Probability Letters
publication date: 1996-04-08T00:00:00Z
review text: The author proves a central limit theorem for \(U\)-statistics under absolute regularity \((\beta\)-mixing). This improves the conditions of \textit{M. Denker} and \textit{G. Keller} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 64, 505-522 (1983; Zbl 0519.60028)] and \textit{K.-i. Yoshihara} [ibid. 35, 237-252 (1976; Zbl 0314.60028)]. Proving this CLT the author uses recent improved limit theorems of \textit{E. Rio} [Ann. Inst. Henri Poincaré, Probab. Stat. 29, No. 4, 587-597 (1993; Zbl 0798.60027)] and \textit{P. Doukhan}, \textit{P. Massart} and \textit{E. Rio} [ibid. 30, No. 1, 63- 82 (1994; Zbl 0790.60037)] for a strictly stationary process and some bound on the remainder terms.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 820291
zbMATH Keywords: \(U\)-statistics
zbMATH Keywords: central limit theorem
zbMATH Keywords: strictly stationary process
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
cites work: On U-statistics and v. mise? statistics for weakly dependent processes
cites work: Mixing: Properties and examples
cites work: The functional central limit theorem for strongly mixing processes
cites work: Weak convergence of partial sums of absolutely regular sequences
cites work: Q5624460
cites work: Q3999009
cites work: Covariance inequalities for strongly mixing processes
cites work: Some Limit Theorems for Random Functions. II
cites work: Limiting behavior of U-statistics for stationary, absolutely regular processes
full work available at URL: 0167-7152(94)00179-c
OpenAlex ID: W2051641685
description: scientific article; zbMATH DE number 820291