Bounding Hellinger Distance with Stein's Method

TL;DR

This paper presents a new explicit bound on the Hellinger distance between a continuous distribution and a Gaussian, with applications to a quantitative central limit theorem and concentration inequalities for U-statistics.

Contribution

It introduces a novel explicit bound on Hellinger distance using Stein's method, enabling new quantitative results in probability theory.

Findings

Derived a quantitative Hellinger CLT.

Established efficient concentration inequalities for U-statistics.

Provided explicit bounds applicable to continuous random variables.

Abstract

This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and efficient concentration inequalities for U-statistics.