Classification of Observations into One of Two Artificially Dichotomized Classes by Using a Normal Screening Variable

Abstract

This article considers a problem of normal based two group classification when the groups are artificially dichotomized by a screening variable. Each group distribution is derived and the best regions for the classification are obtained. These derivations yield yet another classification rule. The rule is studied from several aspects such as the distribution of the rule, the optimal error rate, and the testing of a hypothesis. This article gives relationships among these aspects along with the investigation of the performance of the rule. The classification method and ideas are illustrated in detail with two examples.

Keywords:

• Artificial dichotomization
• Classification
• Doubly truncated multivariate skew-normal distribution
• Optimal error rate

Mathematics Subject Classification:

• Primary 62H30
• Secondary 60E05

Acknowledgment

This research was supported by the Korean Research Foundation Grant funded by the Korean Government (MOEHRD) KRF-2006-311-C00240.