On restricted subset selection for the largest normal mean under heteroscedasticity

Music City Center 

We consider 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, for selecting a nonempty random-size subset of size at most m (0 < m < k ) 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 d, where m, P*, and d are specified in advance of the experiment. The probability of a correct selection and the expected subset size of R are derived. Critical values/procedure parameters that are required for certain k, m, P*, and d are obtained by solving simultaneous integral equations and are presented in tables.

Expected Subset Size


Probability of A Correct Selection

Ranking and Selection

Restricted Subset Selection 

Biopharmaceutical Section