Abstract: Linear and quadratic discriminant analysis are two useful classification methods for which the problem of variable selection is of fundamental importance. To this end, a BIC-type selection criterion (Schwarz (1978)) was recently studied by Raftery and Dean (2006). Despite its usefulness, the BIC's selection consistency (Shao (1997)) was not investigated. To fill this gap, we show that BIC, in conjunction with a backward elimination procedure, is indeed selection consistent. To confirm our asymptotic theory, a number of numerical studies are presented.
Key words and phrases: BIC, discriminant analysis, selection consistency.