Summary
The testing problem is to decide on the basis of repeated independent observations which of the probability densitiesf andg is true. Given upper bounds on the probabilities of error, the object is to minimize the expected sample size if the densityp is true (allowed to differ fromf andg). A characterization of the structure of optimal tests is obtained which is particularly informative in the case wheref,g, andp belong to a Koopman-Darmois family. Ifp=f org, then the optimal tests are sequential probability ratio tests (SPRT's) and a new proof of the well-known optimality property of these tests is obtained as a corollary.
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Research supported by National Science Foundation grant MCS 76-08489
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Lorden, G. Structure of sequential tests minimizing an expected sample size. Z. Wahrscheinlichkeitstheorie verw Gebiete 51, 291–302 (1980). https://doi.org/10.1007/BF00587355
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DOI: https://doi.org/10.1007/BF00587355