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...

Full description

Saved in:
Bibliographic Details
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
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0178-8051
1432-2064
DOI:10.1007/PL00008782