On Hoffmann-Jørgensen’s Inequality for U-Processes

  • Evarist Giné
  • Joel Zinn
Chapter
Part of the Progress in Probability book series (PRPR, volume 30)

Abstract

The object of this note is to prove an analogue for U-processes of (1974) tail inequality for sums of independent symmetric random vectors. The result obtained is best possible in a certain sense but is less useful than the original inequality.

Keywords

ZINN Bonami 

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References

  1. Arcones, M.A. and Giné, E. (1991). Limit theorems for U-processes. Preprint.Google Scholar
  2. Bonami, A. (1970). Etude des coefficients de Fourier des fonctions de L P (G.). Ann. Inst. Fourier 20, 335–402.MathSciNetMATHCrossRefGoogle Scholar
  3. Hitczenko, P. (1988). Comparison of moments for tangent sequences of random variables. Probab. The. Rel Fields 78, 223–230.MathSciNetMATHCrossRefGoogle Scholar
  4. Hoffmann-Jørgensen, J. (1974). Sums of independent Banach space valued random variables. Studia Math. 52, 159–189.MathSciNetGoogle Scholar
  5. Hoffmann-Jørgensen, J. (1977). Probability in Banach spaces. Lecture Notes in Math. 598, 1–186.CrossRefGoogle Scholar
  6. de la Peña, V. (1990). Decoupling and Khintchine’s inequalities for U-statistics. Ann. Probability, to appear.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Evarist Giné
    • 1
  • Joel Zinn
    • 2
  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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