The linear and euclidean discriminant functions: a comparison v1a asymptotic expansions and simulation study

Abstract

This article considers the problem of statistical classification involving multivariate normal populations and compares the performance of the linear discriminant function (LDF) and the Euclidean distance function (EDF), Although the LDF is quite popular and robust, it has been established (Marco, Young and Turner, 1989) that under certain non-trivial conditions, the EDF is equivalent to the LDF, in terms of equal probabilities of misclassifica-tion (error rates). Thus it follows that under those conditions the sample EDF could perform better than the sample LDF, since the sample EDF involves estimation of fewer parameters. Sindation results, also from the above paper; seemed to support this hypothesis. This article compares the two sample discriminant functions through asymptotic expansions of error rates, and identifies situations when the sample EDF should perform better than the sample LDF. Results from simulation experiments are also reported and discussed.