On some classifiers based on multivariate ranks |
| |
Authors: | Olusola Makinde Biman Chakraborty |
| |
Institution: | 1. School of Mathematics, University of Birmingham, Birmingham, United Kingdom;2. Department of Statistics, Federal University of Technology, Akure, Nigeriaosmakinde@futa.edu.ng |
| |
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 |
|
|