Lower Bounds for the Expected Sample Size and the Average Risk of a Sequential Procedure
Sections 1–6 are concerned with lower bounds for the expected sample size, E 0(N), of an arbitrary sequential test whose error probabilities at two parameter points, θ1 and θ2, do not exceed given numbers, α1 and α2, where E 0(N) is evaluated at a third parameter point, θ0. The bounds in (1.3) and (1.4) are shown to be attainable or nearly attainable in certain cases where θ0 lies between θ1 and θ2. In Section 7 lower bounds for the average risk of a general sequential procedure are obtained. In Section 8 these bounds are used to derive further lower bounds for E 0(N) which in general are better than (1.3).