Some Moment and Exponential Inequalities for V-Statistics with Bounded Kernels

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Abstract

This paper provides moment and exponential inequalities for V-statistics with uniformly bounded kernels. The main results are based on moment inequalities for sub-Bernoulli functions of independent random variables. These moment inequalities lead to extensions of the Bernstein inequality to V-statistics. U-statistics are also discussed.

Original languageEnglish (US)
Pages (from-to)511-525
Number of pages15
JournalJournal of Theoretical Probability
Volume14
Issue number2
DOIs
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Keywords

  • Exponential inequality
  • Moment inequality
  • Sub-Bernoulli function
  • Tail probability
  • U-statistic
  • V-statistic

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