Generalization of the Mahalanobis distance in the mixed case
type: Item
instance of: scholarly article
title: Generalization of the Mahalanobis distance in the mixed case
zbMATH Open document ID: 0820.62058
author: Avner Bar-Hen
author: Jean-Jacques Daudin
published in: Journal of Multivariate Analysis
publication date: 1995-09-14T00:00:00Z
review text: In discrimination, as in many multivariate techniques, computation of a distance between two populations is often useful. For example, in taxonomy one can be interested not only in discriminating between two populations but in having an idea of how far apart the populations are. Mahalanobis' \(\Delta^ 2\) has become the standard measure of distance when the observations are quantitative and Hotelling derived its distribution for normal populations. The aim of this article is to adapt these results to the case where the observed characteristics are a mixture of quantitative and qualitative variables. In the first section a generalisation of the Mahalanobis distance is given. Then, in the second section, its asymptotic probability distribution is obtained. In the third section, the rate of convergence and the power of the test are compared through simulation. An example is presented in the last section.
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 769842
zbMATH Keywords: mixture of discrete and continuous variables
zbMATH Keywords: Kullback-Leibler divergence
zbMATH Keywords: location model
zbMATH Keywords: discrimination
zbMATH Keywords: mixture of quantitative and qualitative variables
zbMATH Keywords: generalisation of the Mahalanobis distance
zbMATH Keywords: rate of convergence
zbMATH Keywords: simulation
MaRDI profile type: Publication
full work available at URL: jmva.1995.1040
OpenAlex ID: W2031681694
DOI: 10.1006/JMVA.1995.1040
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description: scientific article; zbMATH DE number 769842