Given several normal populations with unknown means and a common unknown variance, Bechhofer et al. (1954) considered the problem of selecting the population with the largest mean using the indifference zone approach and Tong (1970) considered the problem of constructing a fixed-width confidence interval of the largest mean. They proposed two-stage procedures for their problems. After selection of the population, it would be desirable to get an estimate of the mean. We provide a procedure for selecting the population using the indifference zone approach and simultaneously estimating its mean with a fixed-width interval. Second-order asymptotics of the procedure are also discussed.
Keywords: Ranking and selection; Indifference zone approach; Fixed-width confidence interval; Two-stage procedure
Biography: Yoshikazu Takada is Professor in the Department of Mathematics and Engineering at Kumamoto University (Japan).
He is a member of the Japan Statistical Society, the Mathematical Society of Japan, and the Bernoulli Society.
He received both his M.A. and Ph.D. degrees in mathematical statsitics from Osaka University (Japan).