Alternative Methods of Estimating the Likelihood Ratio in Classification of Multivariate Normal Observations

An observation is to be classified into one of two multivariate normal distributions with equal covariance matrices. When the parameters are unknown, four methods of estimating the likelihood ratio, that is, the plug-in method, the test procedure, the Bayesian approach, and the best invariant estimate method, are reviewed. The assumptions, interpretations, and consequences of the four approaches are given. It is shown that the last three methods yield the same classification procedure.