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

2023/01/05 by Leung, Dennis, Shao, Qi-Man, Zhang, Liqian
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2301.02098

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.

Related

• Nonuniform Berry-Esseen bounds for Studentized U-statistics
• Berry-Esseen theorems for the asymptotic normality of incomplete U-statistics with Bernoulli sampling
• Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms
• Improved nonuniform Berry--Esseen-type bounds
• On the Berry-Esseen bound for the Student statistic