Single-stage interval estimation of the largest normal mean under heteroscedasnoty

Let there be given k(≥1) independent and normally distributed populations where πi has unknown mean μ1 and unknown variance . A single-stage sampling procedure is developed for constructing confidence intervals for the largest of the means. The method is to split up the single sample into two portions, the first consisting of n-1 observations for initial estimation and the second consisting of the remaining one for use as a spare in the final estimation. One-sided, two-sided, and asymptotically optimal confidence interval are considered. A numerical example to apply this procedure is given.