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Published March 1, 1976 | public
Journal Article Open

2-SPRT'S and the modified Kiefer-Weiss problem of minimizing an expected sample size

Lorden, Gary


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.

Additional Information

© 1976 Institute of Mathematical Statistics. Received June 1974; revised July 1975. Research supported by the National Science Foundation under Grant GP-37819. The author is indebted to F. R. Maiocco of the Jet Propulsion Laboratory for his very generous help with the computer calculations. The author also wishes to thank David Siegmund, Tze Lai, and Michael Klass for helpful discussions.


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