Model on a population and prediction on another one: a generalized discriminant rule

Traditionally, discriminant analysis in a decision purpose proceeds in the following manner (McLachlan 1992): A sample is drawn from a population and a partition of this sample in two classes, males and females, is known. Using some variables, an allocation rule is established in order to classify other elements of the previous population. An underlying assumption of this procedure is that the learning sample is representative of the population, i.e. its parameters about the predictive features are statistically not different from the ones of the population.