Rank-Based Classification Using Robust Discriminant Functions

Abstract

In this article, we study ranked discriminant functions that were introduced by Randles et al. (1978a). The ranking method is applied on recently introduced discriminant functions maximum L ₁ depth and quadratic discriminant function based on minimum covariance determinant (MCD) estimates of the mean and covariance. An extensive simulation study shows that not only does the ranking method provide balance between misclassification error rates but it also yields lower total probabilities of misclassification and higher consistency of correct classification for heavy-tailed distributions.

Keywords:

• Minimum covariance determinant
• Misclassification error rate
• Nonparametric classifier
• Statistical depth function

Mathematics Subject Classification:

• 62H30
• 62G35

Acknowledgment

This work is supported by the NSF grant DMS-0604726.