Sufficiency of variables in discrete discriminant analysis

In discrete discriminant analysis the high dimensional estimation problem makes it necessary to restrict oneself to the most effective variables. Conditions are derived to determine whether subsets of variables yield the same optimal allocation rule as the original set. In the discrete case the conditions turn out to be sufficient but not necessary. Tests are derived in the framework of log-linear models. Based on the concept of adequate (α) discriminant sets two variable selection procedures are considered.