A restricted subset selection procedure for selecting the largest normal mean under heteroscedasticity. Issue 1 (2nd January 2023) - Buzaianu, Elena M.; Chen, Pinyuen; Hsu, Lifang
Abstract: This article considers the goal of selecting the population with the largest mean among k normal populations when variances are not known. We propose a Stein-type two-sample procedure, denoted by R BCH, for selecting a nonempty random-size subset of size at most m ( 1 ≤ m ≤ k − 1 ) that contains the population associated with the largest mean, with a guaranteed minimum probability P *, whenever the distance between the largest mean and the second largest mean is at least δ *, where m, P *, and δ * are specified in advance of the experiment. The probability of a correct selection and the expected subset size of R BCH are derived. Critical values/procedure parameters that are required for certain k, m, P *, and δ * are obtained by solving simultaneous integral equations and are presented in tables.