Two Preliminary Tests for Discriminant Analysis

Abstract

ABSTRACT The object of discriminant analysis is to allocate a new individual to one of many a priori known populations. The preliminary test concerns the question whether or not the new individual comes from a new population. Two tests corresponding to such a problem are given in this article; they are developed by the approach proposed by Bar-Hen (1996) in which the asymptotic distribution of the vector of estimated distances between populations play the crucial role. The first test is designed for heteroscedastic multivariate normal populations and utilizes the Bhattacharyya distance, while the second test uses the Mahalanobis distance and is suitable for the homoscedastic case. Although establishing the critical value for a given null hypothesis and chosen significance level requires a solution of multi-integral equation, it can be found simply through Monte Carlo simulations. The performance of the tests is illustrated by some agriculture data resulting from a trial on distinctness among certain varieties of maize.