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March, 1976 2-SPRT'S and The Modified Kiefer-Weiss Problem of Minimizing an Expected Sample Size
Gary Lorden
Ann. Statist. 4(2): 281-291 (March, 1976). DOI: 10.1214/aos/1176343407


A simple combination of one-sided sequential probability ratio tests, called a 2-SPRT, is shown to approximately minimize the expected sample size at a given point $\theta_0$ among all tests with error probabilities controlled at two other points, $\theta_1$ and $\theta_2$. In the symmetric normal and binomial testing problems, this result applies directly to the Kiefer-Weiss problem of minimizing the maximum over $\theta$ of the expected sample size. Extensive computer calculations for the normal case indicate that 2-SPRT's have efficiencies greater than 99% regardless of the size of the error probabilities. Accurate approximations to the error probabilities and expected sample sizes of these tests are given.


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Gary Lorden. "2-SPRT'S and The Modified Kiefer-Weiss Problem of Minimizing an Expected Sample Size." Ann. Statist. 4 (2) 281 - 291, March, 1976.


Published: March, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0367.62099
MathSciNet: MR405750
Digital Object Identifier: 10.1214/aos/1176343407

Primary: 62L10
Secondary: 62F20

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

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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