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

Gary Lorden
The Annals of Statistics
Vol. 4, No. 2 (Mar., 1976), pp. 281-291
Stable URL: http://www.jstor.org/stable/2958202
Page Count: 11
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2-SPRT'S and The Modified Kiefer-Weiss Problem of Minimizing an Expected Sample Size
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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 θ0 among all tests with error probabilities controlled at two other points, θ1 and θ2. In the symmetric normal and binomial testing problems, this result applies directly to the Kiefer-Weiss problem of minimizing the maximum over θ 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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