Distributional and efficiency results for subset selection

Assume k (??k \geq 2) populations are given. The associated independent random variables have continuous distribution functions with an unknown location parameter. The statistical selec??tion goal is to select a non??empty subset which contains the best population,?? that is the pop??ulation with largest value of the location parameter with confi??dence level P* (k^{-1} <P* <1). Some distributional results for subset selection are given and proved. Explicit expressions for expectation and variance of the subset size are presented. Also some distributional and efficiency results are given concerning a generalized selection goal using subset selection. This generalized subset selection goal is to select a non??-empty subset of populations that contains at least one ????\epsilon-best population. An \epsilon-????best population is any population with a parameter value within \epsilon (\epsilon \geq 0) of the largest parameter value. The subset selection goal of Gupta is a special case of the generalized selection goal. Key Words: Selection??; subset selection??; location parameter;?? subset size??; expectation;?? vari??ance??; generalized selection goal.