On some classifiers based on multivariate ranks

ABSTRACT

Non parametric approaches to classification have gained significant attention in the last two decades. In this paper, we propose a classification methodology based on the multivariate rank functions and show that it is a Bayes rule for spherically symmetric distributions with a location shift. We show that a rank-based classifier is equivalent to optimal Bayes rule under suitable conditions. We also present an affine invariant version of the classifier. To accommodate different covariance structures, we construct a classifier based on the central rank region. Asymptotic properties of these classification methods are studied. We illustrate the performance of our proposed methods in comparison to some other depth-based classifiers using simulated and real data sets.

KEYWORDS:

• Error rates
• non parametric classifiers
• rank-based procedures
• rank regions.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H30
• 62G35
• 62G05

Acknowledgment

We are thankful to the anonymous referees and the associate editor whose comments have substantially improved the contents of this paper.

Funding

The research of Olusola Samuel Makinde is partially supported by the Mathematics and Statistics Student Award (University of Birmingham) and Tertiary Education Trust Fund (Federal University of Technology Akure).