Order of magnitude bounds for expectations of A2functions of generalized random bilinear forms
(1998) In Probability Theory and Related Fields 112(4). p.457492 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 nonnegative bilinear forms of nonnegative random variables. The decoupling is achieved by a slight modification of a theorem of de la Peña and Montgomery–Smith (1995).
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1767783
 author
 Klass, Michael J and Nowicki, Krzysztof ^{LU}
 organization
 publishing date
 1998
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 decoupling inequalities, decoupling, generalized random bilinear forms, Ustatistics, expectations of functions, Khintchin's inequality
 in
 Probability Theory and Related Fields
 volume
 112
 issue
 4
 pages
 457  492
 publisher
 Springer
 external identifiers

 scopus:0032259673
 ISSN
 01788051
 language
 English
 LU publication?
 yes
 id
 a1a3be71fbf44fea9cfd9bb60250d2d7 (old id 1767783)
 alternative location
 http://www.jstor.org/stable/2959568
 date added to LUP
 20160401 17:00:21
 date last changed
 20200415 02:28:36
@article{a1a3be71fbf44fea9cfd9bb60250d2d7, 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 nonnegative bilinear forms of nonnegative 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 = {01788051}, language = {eng}, number = {4}, pages = {457492}, publisher = {Springer}, series = {Probability Theory and Related Fields}, title = {Order of magnitude bounds for expectations of A2functions of generalized random bilinear forms}, url = {http://www.jstor.org/stable/2959568}, volume = {112}, year = {1998}, }