On BIC's Selection Consistency for Discriminant Analysis

Linear and/or quadratic discriminant analysis (based on finite Gaussian mixture) is one of the most useful classification methods, for which the problem of variable selection is poorly understood. To fill this important theoretical gap, a novel BIC-type selection criterion in conjunction with a backward elimination procedure is proposed. We show theoretically that the new method is able to identify the true Gaussian structure consistently, even with a heteroscedastic covariance structure. Numerical studies are presented to demonstrate the new method's usefulness.