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March, 1976 Properties of Generalized Sequential Probability Ratio Tests
Bennett Eisenberg, B. K. Ghosh, Gordon Simons
Ann. Statist. 4(2): 237-251 (March, 1976). DOI: 10.1214/aos/1176343404


We consider generalized sequential probability ratio tests (GSPRT's), which are not necessarily based on independent or identically distributed observations, to distinguish between probability measures $P$ and $Q$. It is shown that if $T$ is any test in a wide class of GSPRT's, including all SPRT's, and $T'$ is any rival test possessing error probabilities and sample sizes no greater than those of $T$, then $T'$ must be equivalent to $T$. This notion of optimality of $T$ is weaker than that of Kiefer and Weiss but the results are stronger than theirs. It is also shown that, if an SPRT $T'$ has at least one error probability strictly less than that of another SPRT $T$ with the other error probability no larger, $T'$ requires strictly more observations than $T$ some of the time, under both $P$ and $Q$, and never fewer observations. This assertion generalizes Wijsman's conclusions. The methods used in this paper are quite general, and are different from those of the earlier authors.


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Bennett Eisenberg. B. K. Ghosh. Gordon Simons. "Properties of Generalized Sequential Probability Ratio Tests." Ann. Statist. 4 (2) 237 - 251, March, 1976.


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

zbMATH: 0323.62053
MathSciNet: MR395099
Digital Object Identifier: 10.1214/aos/1176343404

Primary: 62L10

Keywords: Admissibility , Generalized sequential probability ratio test , likelihood ratio , optimality , sequential probability ratio test

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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