On multi-stage procedures for estimating the largest mean of k NOrmal populations having unequal and unknown variances

The problem of constructing confidence interval for the largest of k normal means considered by Saxena and Tong (1969) and Tong (1970, 1973) is extended by considering the case when the populations have unequal and unknown variances. Several multi-stage estimation procedures (like, two-stage, three-stage and accelerated sequential procedures) are developed to deal with the estimation problem. Nice asymptotic properties of these estimation procedures are studied and their relative advantages and disadvantages are discussed.