Discriminant analysis under the common principal components model

Pepler, P.T. , Uys, D.W. and Nel, D.G. (2017) Discriminant analysis under the common principal components model. Communications in Statistics: Simulation and Computation, 46(6), pp. 4812-4827. (doi:10.1080/03610918.2015.1134568)

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Abstract

For two or more populations of which the covariance matrices have a common set of eigenvectors, but different sets of eigenvalues, the common principal components (CPC) model is appropriate. Pepler et al. (2015) proposed a regularised CPC covariance matrix estimator and showed that this estimator outperforms the unbiased and pooled estimators in situations where the CPC model is applicable. This paper extends their work to the context of discriminant analysis for two groups, by plugging the regularised CPC estimator into the ordinary quadratic discriminant function. Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic and linear discriminant analysis. Based on these results, CPC discriminant analysis is recommended for situations where the sample size is small compared to the number of variables, in particular for cases where there is uncertainty about the population covariance matrix structures.

Item Type:Articles
Keywords:Common principal components, Discriminant analysis, Covariance matrix, Monte Carlo simulation
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Pepler, Dr Theo
Authors: Pepler, P.T., Uys, D.W., and Nel, D.G.
College/School:College of Medical Veterinary and Life Sciences > Institute of Biodiversity Animal Health and Comparative Medicine
Journal Name:Communications in Statistics: Simulation and Computation
Publisher:Taylor & Francis
ISSN:0361-0918
ISSN (Online):1532-4141
Published Online:13 January 2016
Copyright Holders:Copyright © 2016 Taylor and Francis
First Published:First published in Communications in Statistics - Simulation and Computation 46(6):4812-4827
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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