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).
Original language | English |
---|---|
Pages (from-to) | 457-492 |
Journal | Probability Theory and Related Fields |
Volume | 112 |
Issue number | 4 |
Publication status | Published - 1998 |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- decoupling inequalities
- decoupling
- generalized random bilinear forms
- U-statistics
- expectations of functions
- Khintchin's inequality