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August 2021 On Charles Stein’s contributions to (in)admissibility
William E. Strawderman
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Ann. Statist. 49(4): 1823-1835 (August 2021). DOI: 10.1214/21-AOS2108

Abstract

Charles Stein made fundamental contributions to admissibility and inadmissibility in estimation and testing. This paper surveys some of the more important ones. Particular attention will be paid to his monumentally important, and at the time, incredibly surprising discovery of the inadmissibility of the usual estimator of the mean in three and higher dimensions. His result on admissibility of Pitman’s estimator of a mean in one and two dimensions, and his results on estimation of a mean matrix and a covariance matrix are also discussed. His work on testing is briefly covered.

Funding Statement

This work was supported by a grant (418098) from the Simons Foundation.

Acknowledgments

The author thanks the Editors for the invitation to contribute to this celebration of one of the most original and truly consequential statisticians of the twentieth century. He thanks Iain Johnstone for providing some of the cited Stanford Technical reports, and Rob Strawderman, and the Associate Editor for carefully reading the manuscript and for helpful suggestions on clarifying the presentation.

Citation

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William E. Strawderman. "On Charles Stein’s contributions to (in)admissibility." Ann. Statist. 49 (4) 1823 - 1835, August 2021. https://doi.org/10.1214/21-AOS2108

Information

Received: 1 December 2020; Revised: 1 June 2021; Published: August 2021
First available in Project Euclid: 29 September 2021

Digital Object Identifier: 10.1214/21-AOS2108

Subjects:
Primary: 62C15 , 62C20
Secondary: 62F10

Keywords: Admissibility , inadmissibility , minimaxity

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 4 • August 2021
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