Classification into One of Two Correlated Normal Populations and Choice of a Suitable Training Sample

Abstract

In standard two class parametric classification problem, a sample unit is classified into one of two classes based on a vector of observations, measured on the sample unit, which follows some distributions for the two classes. The parameters of the distributions are unknown generally and training samples from the populations are used to construct the classifier. The classes are considered to be independent in standard setup. Starting with some motivating examples, we study the problem of classifying an individual into one of two classes when the classes are considered to be dependent under normality assumption of the distributions. Some natural types of training samples in this dependent setup are considered and compared, in terms of probability of correct classification of linear classifier based on those training samples, to suggest the most suitable one.