Projection pursuit discriminant analysis for two groups
In this paper we determine the two groups linear discriminant function which minimizes the total probability of missclassification when a priori probabilities of the two groups are specified. On one hand, this problem is shown to be a special case of the projection pursuit technique in discriminant analysis which provides efficient algorithms for solving optimization of this kind. On the other hand, this linear function is shown to be a generalization of the best linear discriminant function (the version concerned with the total probability of missclassification) introduced by Anderson & Bahadur (1962).Kernel estimation of the discrimination rule and a computer implementation are discussed, and it is shown that the estimate is consistent.