Choosing a Better Training Sample for Classifying an Individual into One of Two Correlated Normal Populations

The problem is to classify a unit into one of two populations which jointly constitute a bivariate normal population N2 (μ1 , μ2, σ 2, σ 2, ρ]. Unlike the usual situation, the populations are not independent but correlated . A matched training sample consists of paired observations only. Earlier studies on classification in correlated setup considered the use of either matched training sample or independent training sample (set of only un-paired observations from each of the two populations). We consider classification problem in correlated setup hased on unbalanced training sample consisting of paired observations as well as single observations from each population. It is observed that probability of correct classification (PCC) of maximum likelihood (ML) rule based on unbalanced training sample is always higher than the minimum of the PCCs based on matched and independent training samples. Moreover, in some cases, it is maxiwnm among the three.