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

Summary, in English

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: Michael J Klass; Krzysztof Nowicki
• Department/s: Department of Statistics
• Publishing year: 1998
• Language: English
• Pages: 457-492
• Publication/Series: Probability Theory and Related Fields
• Volume: 112
• Issue: 4
• Links: http://www.jstor.org/stable/2959568
• Document type: Journal article
• Publisher: Springer
• Topic: Probability Theory and Statistics
• Keywords: decoupling inequalities; decoupling; generalized random bilinear forms; U-statistics; expectations of functions; Khintchin's inequality
• Status: Published
• ISBN/ISSN/Other: ISSN: 0178-8051