On a Conjecture About the Limiting Minimal Efficiency of Sequential Tests

Abstract

For use in comparisons of sequential and nonsequential tests Berk (Ann. Statist. 3 991-998) has defined the limiting relative efficiency of sequential tests as the limiting ratio of the expected sample size under the null hypothesis and the supremum over the parameter set of the expected sample size. He has proved that for the symmetric binomial case the limiting relative efficiency of a class of SPR type tests coincides with a related quantity for SPR tests of drift in a Wiener process. He has also conjectured that this result applies to a more general class. In this note we prove that it holds for exponential families satisfying some mild regularity conditions.