Discrimination with Polychotomous Predictor Variables Using Orthogonal Functions

Abstract

Three discriminant functions proposed by Bahadur (1961 a, b), Martin and Bradley (1972), and Ott and Kronmal (1976) are generalized to accommodate polychotomous predictor variables. The discrete Fourier orthogonal functions used in the generalization provide computational advantages with the use of the fast Fourier transform. Data-dependent inclusion rules for each expansion's coefficients are developed to “smooth” observed frequencies and improve discrimination. The performances of these methods are compared in a simulation study, and populations in which these rules are expected to perform well are identified.