Annals of Statistics

Stein's Paradox is Impossible in Problems with Finite Sample Space

Sam Gutmann

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Abstract

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.

Article information

Source
Ann. Statist., Volume 10, Number 3 (1982), 1017-1020.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345893

Digital Object Identifier
doi:10.1214/aos/1176345893

Mathematical Reviews number (MathSciNet)
MR663454

Zentralblatt MATH identifier
0545.62009

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation

Keywords
Admissible procedures Stein's effect Statistical decision problems

Citation

Gutmann, Sam. Stein's Paradox is Impossible in Problems with Finite Sample Space. Ann. Statist. 10 (1982), no. 3, 1017--1020. doi:10.1214/aos/1176345893. https://projecteuclid.org/euclid.aos/1176345893


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