Efficiency of discriminant analysis when initial samples are classified stochastically

摘要

We consider the problem of discriminant analysis of two multivariate normal populations having a common dispersion matrix, where the initial samples are classified stochastically. We assume a beta model for this classification variable and assume it to be independent of the feature vector X, given the group. We study the Efron efficiency of this procedure compared to the situation where the initial classification is done deterministically and correctly. We present tables and charts of this efficiency and conclude that stochastic supervision contains a great deal of information on the discriminant function.