Multi-stage point and interval estimation of the largest mean ofK normal populations and the associated second-order properties

Abstract

We havek independent normal populations with unknown meansμ1, …,μk and a common unknown varianceσ2. Both point and interval estimation procedures for the largest mean are proposed by means of sequential and three-stage procedures. For the point estimation problem, we require that the maximal risk be at mostW, a preassigned positive number. For the other problem, we wish to construct a fixed-width confidence interval having the confidence coefficient at least 1-α, a preassigned number between zero and one. Asymptotic second order expansions are provided for various characteristics, such as average sample size, associated risks etc., for the suggested multi-stage estimation procedures.