Another Look at Stein’s Method for Studentized Nonlinear Statistics with an Application to U-Statistics

Abstract

AbstractWe 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 out 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.