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August 2021 Stein’s method of normal approximation: Some recollections and reflections
Louis H. Y. Chen
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Ann. Statist. 49(4): 1850-1863 (August 2021). DOI: 10.1214/21-AOS2083

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 It also includes anecdotes of historical interest, including how Stein discovered his method and how I found an unpublished proof of his of the Berry–Esseen theorem.

Acknowledgment

I am thankful to Larry Goldstein and Yu-Kiang Leong for their valuable comments, which helped me improve the exposition of this paper. I am particularly thankful to Larry for his contribution to Section 7. Thanks also go to Adrian Röllin for being always around to render a helping hand whenever I encountered any difficulty with using LaTeX.

Citation

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Louis H. Y. Chen. "Stein’s method of normal approximation: Some recollections and reflections." Ann. Statist. 49 (4) 1850 - 1863, August 2021. https://doi.org/10.1214/21-AOS2083

Information

Received: 1 March 2021; Revised: 1 April 2021; Published: August 2021
First available in Project Euclid: 29 September 2021

Digital Object Identifier: 10.1214/21-AOS2083

Subjects:
Primary: 60F05 , 62E17
Secondary: 60B10

Keywords: concentration inequality , exchangeable pair , Normal approximation , Stein equation , Stein identity , Stein’s method

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 4 • August 2021
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