Exact Density of W Classification Statistic Based on Unmatched Training Sample from Correlated Populations

Summary A unit is to be classified into one of two correlated homoscedastic normal populations by W classification statistic. The two populations are like two different states of a disease. A sample unit can be observed in both the states (populations) . The observations made on the same unit in the two populations are correlated. W is based on an unmatched training sample where N sample units are observed in both the populations and Ni- N units are observed in population i, i = 1, 2. The exact density of W in such set up is derived for unknown means and common dispersion matrix where the correlation linking the populations is known or unknown. Simulated density of W is plotted and probability of correct classification (PCC) is evaluated using simulation.