The Equivalence of Two Rules of Classification for Two Populations
Poole, W. (1980). The Equivalence of Two Rules of Classification for Two Populations. American Statistician, 34(1), 55.
In many applied classification problems, the populations of interest are defined in terms of ranges for the dependent variable. In these situations, it is intuitively appealing to classify individuals into the respective populations based on their estimated conditional expectation. On the other hand, based on theoretical considerations, one may wish to use the classification rule based on the posterior probabilities. This article shows that under certain conditions these two classification rules are equivalent