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March, 1957 A Theory of some Multiple Decision Problems, I
E. L. Lehmann
Ann. Math. Statist. 28(1): 1-25 (March, 1957). DOI: 10.1214/aoms/1177707034


A class of multiple decision procedures is described and its members are shown to possess uniformly minimum risk among all procedures that are unbiased with respect to a certain loss function. This provides a justification for a number of procedures considered by Tukey, Duncan, and others, for certain classes of point estimates, and for some nonparametric decision procedures based on sample cumulative distribution functions and related to tests of the Kolmogoroff-Smirnoff type.


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E. L. Lehmann. "A Theory of some Multiple Decision Problems, I." Ann. Math. Statist. 28 (1) 1 - 25, March, 1957.


Published: March, 1957
First available in Project Euclid: 27 April 2007

MathSciNet: MR84952
zbMATH: 0078.33402
Digital Object Identifier: 10.1214/aoms/1177707034

Rights: Copyright © 1957 Institute of Mathematical Statistics

Vol.28 • No. 1 • March, 1957
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