Categorical FDA under prospective sampling scheme: a proposal for variable selection

Given a population described by p explanatory and one dependent categorical variables, we assume that the dependent variable defines a partition of the population into g groups. Discriminant Analysis studies the relation between the p explanatory variables and the dependent variable finding the subset of variables that has the most predictive power. Generally, in categorical discriminant analysis, the a priori probabilities associated to the g groups are assumed known. In this paper we summarise some suitable approaches under the hypothesis of unknown group a priori probabilities and we propose a new variables selection algorithm.