Another look at Stein's method for Studentized nonlinear statistics with an application to U-statistics

TL;DR

This paper revisits Stein's method to derive uniform Berry-Esseen bounds for Studentized nonlinear statistics, emphasizing censored data and concentration inequalities, with applications to U-statistics.

Contribution

It introduces a new approach using Stein's method for Studentized nonlinear statistics, including censored data and U-statistics, with explicit dependence on kernel degree.

Findings

Established uniform Berry-Esseen bounds for Studentized U-statistics.

Developed an exponential concentration inequality for censored variables.

Highlighted the role of kernel degree in the bounds.

Abstract

We take another look at using Stein's method to establish uniform Berry-Esseen bounds for Studentized nonlinear statistics, highlighting variable censoring and an exponential randomized concentration inequality for a sum of censored variables as the essential tools to carry the arguments involved. As an important application, we prove a uniform Berry-Esseen bound for Studentized U-statistics in a form that exhibits the dependence on the degree of the kernel.