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

Publiceringsår: 1998
Språk: Engelska
Sidor: 457-492
Publikation/Tidskrift/Serie: Probability Theory and Related Fields
Volym: 112
Nummer: 4
Dokumenttyp: Artikel i tidskrift
Förlag: Springer


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).


  • Probability Theory and Statistics
  • decoupling inequalities
  • decoupling
  • generalized random bilinear forms
  • U-statistics
  • expectations of functions
  • Khintchin's inequality


  • ISSN: 0178-8051

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