On Sequential Tests Which Minimize the Maximum Expected Sample Size

Abstract

X ₁, X ₂, …, are independent and identically distributed, the common distribution known except for the value of a parameter θ. The problem is to find a test of H _–1:θ = θ_–1 against H ₁.θ=θ₁, with pre-assigned error probabilities α, β, and which minimizes the maximum expected sample size (the maximum taken with respect to θ). For the cases where α = β and θ is the mean of a normal distribution, and where α = β and θ is a binomial probability and θ_–1 + θ₁ = 1, a computational scheme for finding such a test is described.