Moment and tail estimation for U-statistics with positive kernels

TL;DR

This paper develops non-asymptotic bilateral moment estimates for U-statistics with positive kernels, utilizing degenerate approximation, Bell functions, Poisson distribution properties, and Grand Lebesgue Spaces to improve understanding of their tail behavior.

Contribution

It introduces new non-asymptotic bilateral moment inequalities for U-statistics with positive kernels, combining advanced probabilistic tools and approximation techniques.

Findings

Derived bilateral moment inequalities for U-statistics

Applied Bell functions and Poisson distribution properties

Enhanced tail estimation methods for non-negative random variables

Abstract

We deduce the non-asymptotical (bilateral) estimates for moment inequalities for multiple sums of non-negative (more precisely, non-negative) independent random variables, on the other words, the well known U or V-statistics. Our consideration based on the correspondent estimates for the one-dimensional case by means of the so-called degenerate approximation. We apply also the theory of Bell functions as well as the properties of the Poisson distribution and the theory of the so-called Grand Lebesgue Spaces (GLS).