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December, 1952 Impartial Decision Rules and Sufficient Statistics
Raghu Raj Bahadur, Leo A. Goodman
Ann. Math. Statist. 23(4): 553-562 (December, 1952). DOI: 10.1214/aoms/1177729334


A class of decision problems concerning $k$ populations was considered in [1] and it was shown that a particular decision rule is the uniformly best `impartial' decision rule for many problems of this class. The present paper provides certain improvements of this result. The authors define impartiality in terms of permutations of the $k$ samples rather than in terms of the $k$ ordered values of an arbitrarily chosen real-valued statistic as in the earlier paper. They point out that (under conditions which are satisfied in the standard cases of $k$ independent samples of equal size) if the same function is a sufficient statistic for each of the $k$ samples then the conditional expectation of an impartial decision rule given the $k$ sufficient statistics is also an impartial decision rule. A characterization of impartial decision rules is given which relates the present definition of impartiality with the one adopted in [1]. These results, together with Theorem 1 of [1], yield the desired improvements. The argument indicated here is illustrated by application to a special case.


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Raghu Raj Bahadur. Leo A. Goodman. "Impartial Decision Rules and Sufficient Statistics." Ann. Math. Statist. 23 (4) 553 - 562, December, 1952.


Published: December, 1952
First available in Project Euclid: 28 April 2007

zbMATH: 0048.11902
MathSciNet: MR54909
Digital Object Identifier: 10.1214/aoms/1177729334

Rights: Copyright © 1952 Institute of Mathematical Statistics

Vol.23 • No. 4 • December, 1952
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