Exact exponential tail estimation for sums of independent centered random variables, under natural norming, with applications to the theory of U-statistics

TL;DR

This paper derives precise exponential tail bounds for sums of independent centered random variables using Grand Lebesgue Spaces, with applications to U-statistics, providing refined tail estimates under natural norming.

Contribution

It introduces exact exponential tail estimates for sums of independent centered variables using GLS, and applies these results to improve tail bounds in U-statistics.

Findings

Exact exponential tail bounds for sums of independent variables.

Refined tail estimates for U-statistics under natural norming.

Application of Grand Lebesgue Spaces to tail estimation.

Abstract

We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some applications into the theory of U statistics, where we deduce alike for the independent variables the refined exponential tail estimates for ones under natural norming sequence.