Alternative linear classification rules under order restrictions

Abstract

The Anderson's linear classification rule is used most commonly for the problem of classifying an observation into one of two multinomial 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.

Keywords:

• Anderson's classification rule
• optimal classification rule: miselas-sification probability
• expected cost of misclassification