Approximation and exponential inequalities for sums of dependent random vectors
type: Item
instance of: scholarly article
title: Approximation and exponential inequalities for sums of dependent random vectors
zbMATH Open document ID: 1009.60006
DOI: 10.1016/S1631-073X(02)02242-2
author: Noureddine Rhomari
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2002-08-04T00:00:00Z
review text: An extension of \textit{R. C. Bradley}'s result on coupling of dependent real-valued random variables by independent ones [Mich. Math. J. 30, 69-81 (1983; Zbl 0531.60033)] is obtained for random vectors in \(\mathbb{R}^d\). It allows to establish the exponential inequalities for partial sums of \(\alpha\)-dependent random vectors in \(\mathbb{R}^d\) or their transformations to \(\mathcal{Y}\) where \(\mathcal{Y}\) is a separable Banach or Hilbert space. The Bernstein-type inequalities for partial sums of \(\beta\)-dependent random vectors with values in \(\mathcal{Y}\) are proved as well. Thus the generalizations of some results by \textit{I. F. Pinelis} and \textit{A. I. Sakhanenko} [Theory Probab. Appl. 30, 143-148 (1986); translation from Teor. Veroyatn. Primen. 30, No. 1, 127-131 (1985; Zbl 0568.60028)] and \textit{I. F. Pinelis} [ibid. 35, No. 3, 605-607 (1990), resp. ibid. 35, No. 3, 592-594 (1990; Zbl 0713.62042)] are provided for dependent summands. Several applications are given, including estimation of convergence rates in the SLLN for absolutely regular processes with values in \(\mathcal{Y}\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 1744370
zbMATH Keywords: random vectors
zbMATH Keywords: mixing coefficients
zbMATH Keywords: Banach and Hilbert spaces
zbMATH Keywords: partial sums
zbMATH Keywords: exponential inequalities
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
cites work: Q3886625
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description: scientific article; zbMATH DE number 1744370