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Published January 1, 1977 | public
Journal Article Open

Nearly-optimal sequential tests for finitely many parameter values

Lorden, Gary


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% are obtained in some "small-sample" cases.

Additional Information

© 1977 Institute of Mathematical Statistics. Received December 1974; revised June 1976. Research supported by the National Science Foundation under Grant GP-37819.The author is grateful to David Siegmund and Michael Klass for stimulating and helpful conversations, to the Associate Editor for a careful reading of the manuscript and useful suggestions, and especially to Jack Kiefer for his enthusiastic and inspiring guidance of the author's thesis research, of which the present work is an outgrowth.


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