Asymptotic Comparison of Two Discriminants Used in Normal Covariate Classification

Abstract

In this paper, we examine the performance of Anderson's classification statistic with covariate adjustment in comparison with the usual Anderson's classification statistic without covariate adjustment in a two-population normal covariate classification problem. The same problem has been investigated using different methods of comparison by some authors. See the bibliography. The aim of this paper is to give a direct comparison based upon the asymptotic probabilities of misclassification. It is shown that for large equal sample size of a training sample from each population, Anderson's classification statistic with covariate adjustment and cut-off point equal to zero, has better performance.

Keywords:

• covariate classification
• Anderson's classification statistic with covariate adjustment
• probabilities of misclassification
• asymptotic expansions