A distribution-free discrimination procedure based on clustering

A method is presented for constructing distribution-free tolerance regions for one distribution based on the clusters of the sample from a second distribution. The tolerance regions are constructed so as to minimize the probability of reserve judgment in a two-class discrimination procedure that allows the conditional error probabilities to be controlled within prescribed upper bounds. The method results in discrimination functions that are easily implemented on a computer. Although the method is not, in general, consistent with optimal procedures, it is appealing for high-dimensional problems with multimodal distributions.