The Edgeworth Expansion for U-Statistics of Degree Two

  • P. J. Bickel
  • F. Götze
  • W. R. van Zwet
Open Access
Chapter
Part of the Selected Works in Probability and Statistics book series (SWPS)

Abstract

An Edgeworth expansion with remainder o(N−1) is established for a U-statistic with a kernel h of degree 2. The assumptions involved appear to be very mild; in particular, the common distribution of the summands h(X i , X j ) is not assumed to be smooth.

Key words and phrases

Edgeworth expansion second order asymptotics U-statistics 

Reference

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • P. J. Bickel
    • 1
    • 2
    • 3
  • F. Götze
    • 1
    • 2
    • 3
  • W. R. van Zwet
    • 1
    • 2
    • 3
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.University of BielefeldBielefeldGermany
  3. 3.University of LeidenLeidenUSA

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