Asymptotic Results for Discriminant Analysis When the Initial Samples are Misclassified

Abstract

The effect of misclassification, for initial samples of finite size from multivariate normal populations, on the linear discriminant function (Anderson's classification statistic [l]) has been considered by analysing the results of sampling experiments. (Lachenbruch [2]). This paper presents an alternative approach by which the effect of misclassification is expressed in the form of asymptotic expansions of degrees higher than previously available. Although the results of these expansions are not always in agreement with the conclusions drawn by Lachenbruch from his sampling experiments in which the sample size was moderately large, the conclusion from the asymptotic approach is that Lachenbruch's large sample results (obtained when the sample size is infinite) hold in most cases. In those instances in which they apparently do not, a general condition for them to hold is obtained.