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

Research output: Contribution to journalArticle

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

Fingerprint

Moment Inequalities
Exponential Inequality
kernel
Statistics
Bernstein Inequality
U-statistics
Independent Random Variables
Bernoulli
Kernel
Moment inequalities
Random variables

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

Cite this

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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.",
keywords = "Exponential inequality, Moment inequality, Sub-Bernoulli function, Tail probability, U-statistic, V-statistic",
author = "Cunhui Zhang",
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volume = "14",
pages = "511--525",
journal = "Journal of Theoretical Probability",
issn = "0894-9840",
publisher = "Springer New York",
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}

Some Moment and Exponential Inequalities for V-Statistics with Bounded Kernels. / Zhang, Cunhui.

In: Journal of Theoretical Probability, Vol. 14, No. 2, 01.12.2001, p. 511-525.

Research output: Contribution to journalArticle

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