We consider the problem of discriminating between two independent multivariate normal populations, Np(μ1, ∑1) and Np(μ2, ∑2), having distinct mean vectors μ1 and μ2 and distinct covariance matrices ∑1 and ∑2. The parameters μ1, μ2, μ1, and ∑2 are unknown and are estimated by means of independent random training samples from each population. We derive a stochastic representation for the exact distribution of the "plug-in" quadratic discriminant function for classifying a new observation between the two populations. The stochastic representation involves only the classical standard normal, chi-square, and F distributions and is easily implemented for simulation purposes. Using Monte Carlo simulation of the stochastic representation we provide applications to the estimation of misclassification probabilities for the well-known iris data studied by Fisher (Ann. Eugen. 7 (1936), 179-188); a data set on corporate financial ratios provided by Johnson and Wichern (Applied Multivariate Statistical Analysis, 4th ed., Prentice-Hall, Englewood Cliffs, NJ, 1998); and a data set analyzed by Reaven and Miller (Diabetologia 16 (1979), 17-24) in a classification of diabetic status.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty