Nearly-Optimal Sequential Tests for Finitely Many Parameter Values
The Annals of Statistics · 1977 · Volume 5 · Issue 1
Abstract
Combinations of one-sided sequential probability ratio tests (SPRT's) are shown to be "nearly optimal" for problems involving a finite number of possible underlying distributions. Subject to error probability constraints, expected sample sizes (or weighted averages of them) are minimized to within $o(1)$ asymptotically. For sequential decision problems, simple explicit procedures are proposed which "do exactly what a Bayes solution would do" with probability approaching one as the cost per observation, $c$, goes to zero. Exact computations for a binomial testing problem show that efficiencies of about 97${\tt\%}$ are obtained in some "small-sample" cases.
Keywords
62F20, 62L10, asymptotic optimality, Bayes solution, sequential probability ratio test
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