| Abstract: | Summary The problem of selecting a subpopulation from a given populationII is to be, on the basis of measurements of members ofII, achieved by choosing those members ofII who satisfy the standards determined by a given selection cirterion and rejecting those who do not.
Since the optimum selection depends on the unknown parameter of the probability distribution ofII, it is here considered how to construct a decision function from the space of subsidiary sample having infor-mation on θ
to the space of selections. Thus the existence of Bayes and minimax decision functions under the constraint defined by the
selection criterion is proved. A necessary and sufficient condition for a decision function satisfying the constraint to be
a Bayes decision function is also obtained.
The Institute of Statistical Mathematics |
