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December, 1982 Adaptive Procedures in Multiple Decision Problems and Hypothesis Testing
Andrew L. Rukhin
Ann. Statist. 10(4): 1148-1162 (December, 1982). DOI: 10.1214/aos/1176345980


Necessary and sufficient conditions for the existence of adaptive procedures for identification of one of several probability distributions or for testing a simple hypothesis against a simple alternative are obtained. By definition, adaptive procedures are required to exhibit the same asymptotic behavior for several parametric families as do the optimal (minimax) estimators for each of these families. The proofs are based on a multivariate version of Chernoff's theorem, providing asymptotic formulas for probabilities of large deviations for sums of i.i.d. random vectors. Some examples of adaptive procedures are considered, and the non-existence of such rules is established in certain situations.


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Andrew L. Rukhin. "Adaptive Procedures in Multiple Decision Problems and Hypothesis Testing." Ann. Statist. 10 (4) 1148 - 1162, December, 1982.


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

zbMATH: 0512.62046
MathSciNet: MR673650
Digital Object Identifier: 10.1214/aos/1176345980

Primary: 62F35
Secondary: 60F10 , 62F05 , 62F12

Keywords: Adaptive procedures , Multiple decision problem with finite parameter space , multivariate Chernoff's theorem , probability of incorrect decision , testing of simple hypothesis

Rights: Copyright © 1982 Institute of Mathematical Statistics


Vol.10 • No. 4 • December, 1982
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