Stein's method of normal approximation: Some recollections and reflections

TL;DR

This paper provides a personal overview of Stein's method for normal approximation, highlighting its characterization, construction of Stein identities, diverse applications, and historical anecdotes.

Contribution

It offers a reflective exposition on Stein's method, emphasizing its construction, applications, and historical development from the author's personal perspective.

Findings

Multiple approaches to constructing Stein identities

Applications to various mathematical problems

Historical insights into Stein's method and the Berry-Esseen theorem

Abstract

This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it provides glimpses into the many approaches to constructing Stein identities and the diverse applications of Stein's method to mathematical problems. It also includes anecdotes of historical interest, including how Stein discovered his method and how I found an unpublished proof of his of the Berry-Esseen theorem.