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Order of magnitude bounds for expectations of A2-functions of generalized random bilinear forms

Klass, Michael J and Nowicki, Krzysztof LU (1998) In Probability Theory and Related Fields 112(4). p.457-492
Abstract
Let Φ be a symmetric function, nondecreasing on [0,∞) and satisfying a Δ2 growth condition, (X 1,Y 1), (X 2,Y 2),…,(X n ,Y n ) be arbitrary independent random vectors such that for any given i either Y i =X i or Y i is independent of all the other variates. The purpose of this paper is to develop an approximation of valid for any constants {a ij }1≤ i,j≤n , {b i } i =1 n , {c j } j =1 n and d. Our approach relies primarily on a chain of successive extensions of Khintchin's inequality for decoupled random variables and the result of Klass and Nowicki (1997) for non-negative bilinear forms of non-negative random variables. The decoupling is achieved by a slight modification of a theorem of de la Peña and Montgomery–Smith (1995).
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
decoupling inequalities, decoupling, generalized random bilinear forms, U-statistics, expectations of functions, Khintchin's inequality
in
Probability Theory and Related Fields
volume
112
issue
4
pages
457 - 492
publisher
Springer
ISSN
0178-8051
language
English
LU publication?
yes
id
a1a3be71-fbf4-4fea-9cfd-9bb60250d2d7 (old id 1767783)
alternative location
http://www.jstor.org/stable/2959568
date added to LUP
2011-01-27 14:46:35
date last changed
2016-04-16 05:12:36
@article{a1a3be71-fbf4-4fea-9cfd-9bb60250d2d7,
  abstract     = {Let Φ be a symmetric function, nondecreasing on [0,∞) and satisfying a Δ2 growth condition, (X 1,Y 1), (X 2,Y 2),…,(X n ,Y n ) be arbitrary independent random vectors such that for any given i either Y i =X i or Y i is independent of all the other variates. The purpose of this paper is to develop an approximation of valid for any constants {a ij }1≤ i,j≤n , {b i } i =1 n , {c j } j =1 n and d. Our approach relies primarily on a chain of successive extensions of Khintchin's inequality for decoupled random variables and the result of Klass and Nowicki (1997) for non-negative bilinear forms of non-negative random variables. The decoupling is achieved by a slight modification of a theorem of de la Peña and Montgomery–Smith (1995).},
  author       = {Klass, Michael J and Nowicki, Krzysztof},
  issn         = {0178-8051},
  keyword      = {decoupling inequalities,decoupling,generalized random bilinear forms,U-statistics,expectations of functions,Khintchin's inequality},
  language     = {eng},
  number       = {4},
  pages        = {457--492},
  publisher    = {Springer},
  series       = {Probability Theory and Related Fields},
  title        = {Order of magnitude bounds for expectations of A2-functions of generalized random bilinear forms},
  volume       = {112},
  year         = {1998},
}