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September, 1982 Stein's Paradox is Impossible in Problems with Finite Sample Space
Sam Gutmann
Ann. Statist. 10(3): 1017-1020 (September, 1982). DOI: 10.1214/aos/1176345893


The use of admissible procedures in each of several problems may be inadmissible when the problems are combined, in the sense of summed loss. Thus apparently irrelevant information can sometimes be used to reduce risk over the entire parameter space. This is known as Stein's Paradox. We prove here that this cannot occur when the sample spaces for the problems are finite.


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Sam Gutmann. "Stein's Paradox is Impossible in Problems with Finite Sample Space." Ann. Statist. 10 (3) 1017 - 1020, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0545.62009
MathSciNet: MR663454
Digital Object Identifier: 10.1214/aos/1176345893

Primary: 62C15
Secondary: 62F10

Keywords: Admissible procedures , Statistical decision problems , Stein's effect

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • September, 1982
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