Berry-Esseen Bounds for Studentized Statistics by Stein's Method.

摘要

The Stein's method, originally introduced by Stein (1972), gives us a novel way to investigate normal approximation. This method has since been developed in different areas and can be applied to different distributional approximations. It is a very powerful tool to estimate the absolute error of approximations and also the relative error.;In this thesis, we establish the uniform and non-uniform Berry-Esseen bound for a class of Studentized statistics via Stein's method. In particular, we recover the optimal results for Student's t-statistics, Studentized U-statistics and Studentized L-statistics.