Rosenthal's inequality for LPQD sequences
type: Item
instance of: scholarly article
title: Rosenthal's inequality for LPQD sequences
zbMATH Open document ID: 0931.60007
DOI: 10.1016/S0167-7152(98)00199-0
author: Sana Louhichi
published in: Statistics \& Probability Letters
publication date: 2000-03-08T00:00:00Z
review text: Let \((X_n)_{n\in\mathbb{N}}\) be a sequence of centered r.v.'s. Let \(S_n= X_1+ X_2+\cdots+ X_n\) and \(S_{m,n}= S_{m+n}- S_m\) with the convention that \(S_0= 0\). Suppose that the sequence \((X_n)_{n\in\mathbb{N}}\) has a finite moment of order \(r>2\). \textit{T. Birkel} [Ann. Probab. 16, No. 3, 1184-1193 (1988; Zbl 0647.60039)] showed that the Marcinkiewicz-Zygmund inequality \(A_r(n):= \sup_{m\in\mathbb{N}} E|S_{m,n}|^r\leq O(n^{r/2})\), \(n\to\infty\), holds for associated sequences. Along the line of Birkel Rosenthal's inequalities for linearly positive quadrant dependent random variables are considered. A generalization is obtained.
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 1271606
zbMATH Keywords: moment inequalities
zbMATH Keywords: Rosenthal's inequality
zbMATH Keywords: LPQD sequences
zbMATH Keywords: associated sequences
reviewed by: Ludwig Paditz
MaRDI profile type: Publication
cites work: Moment bounds for associated sequences
cites work: A functional central limit theorem for positively dependent random variables
cites work: Mixing: Properties and examples
cites work: Association of Random Variables, with Applications
cites work: Independence via uncorrelatedness under certain dependence structures
cites work: Some Concepts of Dependence
cites work: Q4327561
cites work: Q4084474
full work available at URL: s0167-7152(98)00199-0
OpenAlex ID: W2009161859
description: scientific article; zbMATH DE number 1271606