A non-uniform Berry-Esseen bound via Stein's method

This paper is part of our efforts to develop Stein's method beyond uniform bounds in normal approximation. Our main result is a proof for a non-uniform Berry–Esseen bound for independent and not necessarily identically distributed random variables without assuming the existence of third moments...

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Published in:Probability theory and related fields 2001-06, Vol.120 (2), p.236-254
Main Authors: CHEN, Louis H. Y, SHAO, Qi-Man
Format: Article
Language:English
Subjects:
Exact sciences and technology
Limit theorems
Mathematics
Probability
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Stochastic processes
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SHAO, Qi-Man
description This paper is part of our efforts to develop Stein's method beyond uniform bounds in normal approximation. Our main result is a proof for a non-uniform Berry–Esseen bound for independent and not necessarily identically distributed random variables without assuming the existence of third moments. It is proved by combining truncation with Stein's method and by taking the concentration inequality approach, improved and adapted for non-uniform bounds. To illustrate the technique, we give a proof for a uniform Berry–Esseen bound without assuming the existence of third moments.
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subjects Exact sciences and technology
Limit theorems
Mathematics
Probability
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Stochastic processes
title A non-uniform Berry-Esseen bound via Stein's method
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