Structure of sequential tests minimizing an expected sample size

Abstract

The testing problem is to decide on the basis of repeated independent observations which of the probability densities f and g is true. Given upper bounds on the probabilities of error, the object is to minimize the expected sample size if the density p is true (allowed to differ from f and g). A characterization of the structure of optimal tests is obtained which is particularly informative in the case where f, g, and p belong to a Koopman-Darmois family. If p=f or g, 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. © 1980 Springer-Verlag.