Open Access
November 2019 Larry Brown’s Work on Admissibility
Iain M. Johnstone
Statist. Sci. 34(4): 657-668 (November 2019). DOI: 10.1214/19-STS744


Many papers in the early part of Brown’s career focused on the admissibility or otherwise of estimators of a vector parameter. He established that inadmissibility of invariant estimators in three and higher dimensions is a general phenomenon, and found deep and beautiful connections between admissibility and other areas of mathematics. This review touches on several of his major contributions, with a focus on his celebrated 1971 paper connecting admissibility, recurrence and elliptic partial differential equations.


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Iain M. Johnstone. "Larry Brown’s Work on Admissibility." Statist. Sci. 34 (4) 657 - 668, November 2019.


Published: November 2019
First available in Project Euclid: 8 January 2020

zbMATH: 07240221
MathSciNet: MR4048596
Digital Object Identifier: 10.1214/19-STS744

Keywords: best invariant estimator , Blyth’s method , Brownian diffusion , Complete class theorems , differential inequality , elliptic partial differential equation , inadmissibility , James–Stein estimator , loss function , recurrence , variational problem

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.34 • No. 4 • November 2019
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