The Annals of Statistics

Properties of Generalized Sequential Probability Ratio Tests

Bennett Eisenberg, B. K. Ghosh, and Gordon Simons

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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.

Article information

Ann. Statist., Volume 4, Number 2 (1976), 237-251.

First available in Project Euclid: 12 April 2007

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Primary: 62L10: Sequential analysis

Generalized sequential probability ratio test admissibility optimality sequential probability ratio test likelihood ratio


Eisenberg, Bennett; Ghosh, B. K.; Simons, Gordon. Properties of Generalized Sequential Probability Ratio Tests. Ann. Statist. 4 (1976), no. 2, 237--251. doi:10.1214/aos/1176343404.

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