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January, 1977 Nearly-Optimal Sequential Tests for Finitely Many Parameter Values
Gary Lorden
Ann. Statist. 5(1): 1-21 (January, 1977). DOI: 10.1214/aos/1176343737


Combinations of one-sided sequential probability ratio tests (SPRT's) are shown to be "nearly optimal" for problems involving a finite number of possible underlying distributions. Subject to error probability constraints, expected sample sizes (or weighted averages of them) are minimized to within $o(1)$ asymptotically. For sequential decision problems, simple explicit procedures are proposed which "do exactly what a Bayes solution would do" with probability approaching one as the cost per observation, $c$, goes to zero. Exact computations for a binomial testing problem show that efficiencies of about 97${\tt\%}$ are obtained in some "small-sample" cases.


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Gary Lorden. "Nearly-Optimal Sequential Tests for Finitely Many Parameter Values." Ann. Statist. 5 (1) 1 - 21, January, 1977.


Published: January, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0386.62070
MathSciNet: MR438610
Digital Object Identifier: 10.1214/aos/1176343737

Primary: 62L10
Secondary: 62F20

Keywords: asymptotic optimality , Bayes solution , sequential probability ratio test

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • January, 1977
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