The studentized location linear discriminant function

The location linear discriminant function is used in a two-population classification problem when the available data are generated from both binary and continuous random variables. Asymptotic distribution of the studentized location linear discriminant function is derived directly without the inversion of the corresponding characteristic function. The resulting plug-in estimate of the overall error of misclassification consists of the estimate based on the limiting distribution of the discriminant plus a correction term up to the second order. By comparison, our estimate avoids exact knowledge of the Mahalanobis distances which is necessary when the expansions of Vlachonikolis (1985) are used in the case of an arbitrary cut-off point. An example is re-examined and analysed in the present context.