Two-Stage Procedure Having Exact Third-Order Properties for a Normal Mean

Abstract

We consider the problem of fixed-width confidence interval estimation of mean μ of a normal distribution with unknown variance σ2 under an additional assumption that the unknown variance σ2 has a known lower bound . We deal with the two-stage procedure proposed by Mukhopadhyay and Duggan (1997) and provide “exact” third-order approximations to the average sample size and the coverage probability with guaranteeing exact consistency. It turns out that the exact third-order approximation gives explicit relations between the coverage probability and the lower bound σ L and that it is superior to the second-order approximation in accuracy via some simulation results.