AN EXPERIMENTAL COMPARISON OF STATISTICAL AND LINEAR PROGRAMMING APPROACHES TO THE DISCRIMINANT PROBLEM

Abstract

ABSTRACT This paper reports the results of an experimental comparison of three linear programming approaches and the Fisher procedure for the discriminant problem. The linear programming approaches include two formulations proposed by Freed and Glover and a newly proposed mixed‐integer, linear goal programming formulation. Ten test problems were generated for each of the 36 cells in the three‐factor, full‐factorial experimental design. Each test problem consisted of a 30‐case estimation sample and a 1,000‐case holdout sample. Experimental results indicate that each of the four approaches was statistically preferable in certain cells of the experimental design. Sample‐based rules are suggested for selecting an approach based on Hotelling's T 2 and Box's M statistics. Subject Areas: Statistical Techniques, Linear Statistical Models, and Linear Programming.