On Some Nonparametric Classifiers Based on Distribution Functions of Multivariate Ranks

Olusola Samuel Makinde () and Biman Chakraborty ()
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Olusola Samuel Makinde: University of Birmingham, School of Mathematics
Biman Chakraborty: University of Birmingham, School of Mathematics

Chapter Chapter 15 in Modern Nonparametric, Robust and Multivariate Methods, 2015, pp 249-264 from Springer

Abstract: Abstract 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.

Keywords: Bayes risk; Elliptically symmetric distributions; Location shift; Maximal depth; Spatial outlyingness (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22404-6_15

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DOI: 10.1007/978-3-319-22404-6_15

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