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.
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Noda, K. Optimal construction of a selection of a subpopulation. Ann Inst Stat Math 37, 415–435 (1985). https://doi.org/10.1007/BF02481110
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DOI: https://doi.org/10.1007/BF02481110