An Estimation Problem Relating to Subset Selection for Normal Populations.

Let p sub 1, p sub 2,..., pi sub k be k independent normal populations with unknown means theta sub 1, theta sub 2,..., theta sub k, respectively, and a common known variance tau sub 2. The population associated with the largest theta sub i is called the best population. In the subset selection approach, the authors want to select a nonempty subset of the k populations so that it includes the best population with a minimum guaranteed probability. The basic idea of the subset selection approach is that the number of populations to be selected should depend upon the evidence supplied by the data.