The functional limit theorem for the canonical \(U\)-processes defined on dependent trials
type: Item
instance of: scholarly article
title: The functional limit theorem for the canonical \(U\)-processes defined on dependent trials
zbMATH Open document ID: 1242.62015
DOI: 10.1134/S0037446611040045
author: Igor S. Borisov
author: V. A. Zhechev
published in: Siberian Mathematical Journal
publication date: 2011-10-25T00:00:00Z
review text: This paper provides a functional limit theorem for canonical \(U\)-statistics of arbitrary order based on a stationary sequence of \(\varphi\)-mixing random variables. The result complements the weak limit theorem for canonical \(U\)-statistics of \textit{I. S. Borisov} and \textit{N. V. Volod'ko} [Mat. Tr. 11, No. 1, 25--48 (2008); translation in Sib. Adv. Math. 18, No. 4, 242--257 (2008; Zbl 1249.60027)]. The proof relies on an orthonormal representation of the kernel function associated with the statistic and the limit distribution is described in terms of a linear combination of products of Hermite polynomials evaluated at a sequence of dependent Wiener processes with a known covariance structure.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 5963627
zbMATH Keywords: invariance principle
zbMATH Keywords: stationary sequences
zbMATH Keywords: \(\varphi\)-mixing
reviewed by: Neville Weber
MaRDI profile type: Publication
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full work available at URL: s0037446611040045
OpenAlex ID: W2115340730
description: scientific article; zbMATH DE number 5963627