Open Access
September, 1952 The use of Previous Experience in Reaching Statistical Decisions
J. L. Hodges Jr., E. L. Lehmann
Ann. Math. Statist. 23(3): 396-407 (September, 1952). DOI: 10.1214/aoms/1177729384


Instead of minimizing the maximum risk it is proposed to restrict attention to decision procedures whose maximum risk does not exceed the minimax risk by more than a given amount. Subject to this restriction one may wish to minimize the average risk with respect to some guessed a priori distribution suggested by previous experience. It is shown how Wald's minimax theory can be modified to yield analogous results concerning such restricted Bayes solutions. A number of examples are discussed, and some extensions of the above criterion are briefly considered.


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J. L. Hodges Jr.. E. L. Lehmann. "The use of Previous Experience in Reaching Statistical Decisions." Ann. Math. Statist. 23 (3) 396 - 407, September, 1952.


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

zbMATH: 0047.38306
MathSciNet: MR50240
Digital Object Identifier: 10.1214/aoms/1177729384

Rights: Copyright © 1952 Institute of Mathematical Statistics

Vol.23 • No. 3 • September, 1952
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