The Annals of Statistics

2-SPRT'S and The Modified Kiefer-Weiss Problem of Minimizing an Expected Sample Size

Gary Lorden

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Abstract

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.

Article information

Source
Ann. Statist. Volume 4, Number 2 (1976), 281-291.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176343407

Digital Object Identifier
doi:10.1214/aos/1176343407

Mathematical Reviews number (MathSciNet)
MR405750

Zentralblatt MATH identifier
0367.62099

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis
Secondary: 62F20

Keywords
Sequential probability ratio test Bayes solution asymptotic optimality

Citation

Lorden, Gary. 2-SPRT'S and The Modified Kiefer-Weiss Problem of Minimizing an Expected Sample Size. Ann. Statist. 4 (1976), no. 2, 281--291. doi:10.1214/aos/1176343407. http://projecteuclid.org/euclid.aos/1176343407.


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