Nonparametric methods in multivariate discriminant analysis

Abstract

Nonparametric analogs to Wilk's [Lambda], Pillai's V, and Hotelling's T [superscript 2, subscript 0] are proposed as multivariate discriminators. Small sample distributions for the proposed statistics are generated by a method based on ranks. Simulation studies are made comparing parametric versus nonparametric methods on the basis of probability of misclassification under an assumption of normality of the data, and also when the assumption of normality of the data is violated. An investigation is made of methods for evaluating the relative discriminatory power of subsets of variables in a management discriminant analysis problem. Seven different selection methods are compared for both the parametric approach and the nonparametric method of ranking the data.