Linear Discriminant Functions for Stationary Time Series

Optimal classification rules based on linear functions which maximize the Chernoff distance, or the Morisita distance, or the Kullback-Leibler distance are studied here. We obtain an expression for the optimal linear discriminant function and show that the resulting linear procedure belongs to the Anderson-Bahadur admissible class. For the comparison of discriminant rules we use some index which is the measure of the accuracy of a given class of discriminant procedures. The asymptotic form of the discriminant function is also studied.