Order of magnitude bounds for expectations of A2-functions of generalized random bilinear forms
(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).
Please use this url to cite or link to this publication:
http://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, 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}, }