On some nonparametric classifiers based on distribution functions of multivariate ranks

Olusola Samuel Makinde, Biman Chakraborty*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Citations (Scopus)


Over the last two decades, multivariate sign and rank based methods have become popular in analysing multivariate data. In this paper, we propose a classification methodology based on the distribution of multivariate rank functions. The proposed method is fully nonparametric in nature. Initially, we consider a theoretical version of the classifier for K populations and show that it is equivalent to the Bayes rule for spherically symmetric distributions with a location shift. Then we present the empirical version of that and show that the apparent misclassification rate of the empirical version of the classifier converges asymptotically to the Bayes risk. We also present an affine invariant version of the classifier and its optimality for elliptically symmetric distributions. We illustrate the performance in comparison with some other depth based classifiers using simulated and real data sets.

Original languageEnglish
Title of host publicationModern Nonparametric, Robust and Multivariate Methods
Subtitle of host publicationFestschrift in Honour of Hannu Oja
Number of pages16
ISBN (Electronic)9783319224046
ISBN (Print)9783319224039
Publication statusPublished - 1 Jan 2015


  • Bayes risk
  • Elliptically symmetric distributions
  • Location shift
  • Maximal depth
  • Spatial outlyingness

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


Dive into the research topics of 'On some nonparametric classifiers based on distribution functions of multivariate ranks'. Together they form a unique fingerprint.

Cite this