Abstract
A decision function _??_*n which takes the place of an optimum selection φ* of a subpopulation (or a subset) of individuals from a population is given on the basis of a kernel-type estimator _??_n of a regression function η, where _??_n has the form similar to the Perzen Kernel-type density estimator. Further the risk of _??_ is evaluated with a given sample size n. As a preparation of the above-mentioned result, an integration of the mean square error of _??_n is also evaluated.
