  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.
