Multi-Stage Interval Estimations of the Largest Mean of k Normal Populations

Summary We have k normal populations (k ⩾ 1) with means θ1, θ2, …, θk and a common unknown variance σ2. A fixed-width confidence interval for θ*=max⁡1≤i≤k θi is desired so that the coverage probability is at least γ (preassigned) for every θ = (θ1, θ2, …, θk) and σ2 > 0. A class of multistage procedures is considered for the solution of this problem. It is shown that at least for k ≤ 2, the efficiencies of those procedures are always less than one.