The Performance of the Linear Discriminant Function in Nonoptimal Situations and the Estimation of Classification Error Rates: A Review of Recent Findings

This article is a review of the results, as are available, on the performance of the linear discriminant function in situations where the assumptions of multivariate normality and equal group dispersion structures are violated. Some new results are discussed for the case of classification using discrete variables, and in the case of both binary and continuous variables. In addition, alternative methods which have been proposed, and evaluated, for estimating misclassification error rates are thoroughly reviewed. In all cases, the material is reviewed in terms of practical significance, with particular emphasis on the conditions unfavorable to the performance of each procedure.