Summary: T. W. Anderson’s linear classification rule [An introduction to multivariate statistical analysis. (1958; Zbl 0083.14601)] is used most commonly for the problem of classifying an observation into one of two multinormal populations with a common covariance matrix. Unfortunately, this rule often has been shown to perform poorly in high dimensions. Promising alternatives to Anderson’s rule have been proposed under various situations.
This article suggests alternatives by using different estimates for the usual (plug-in) mean estimates under order restrictions. The performance of the proposed rules with the consideration of the accuracy of the classification is examined both theoretically and through simulation. Our results indicate that some improvements over Anderson’s rule can be achieved under order restrictions.