Sharp moment and exponential tail estimates for U-statistics

Abstract

We obtain in this paper a non-asymptotic non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for U-statistics by means of martingale representation. We show also the exactness of obtained estimations in one way or another by providing appropriate examples.

References in corpus (3)

• Schlomilch and Bell Series for Bessel's Functions, with Probabilistic Applications
• Sharp moment estimates for polynomial martingales
• Banach spaces characterization of random vectors with exponential decreasing tails of distribution

Cited by in corpus (3)

• Uniform Limit Theorem and tail estimates for parametric u-statistics
• Moment and tail estimation for U-statistics with positive kernels
• Moment and tail estimates and Banach space valued Non-Central Limit Theorem (NCLT) for sums of multi-indexed random variables, processes and fields