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, E₀(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 E₀(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 E₀(N) which in general are better than (1.3).