The linear and euclidean discriminant functions: a comparison v1a asymptotic expansions and simulation study |
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Authors: | J P Koolaard C R O Lawoko |
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Institution: | 1. Biometrics Unit , NZ Institute for Crop and Food Research , Private Bag, Levin, 4005, New Zealand;2. Faculty of Business , Queensland University of Technology , Gardens Point Campus, GPO Box 2434, Brisbane, QLD, 4001, Australia |
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Abstract: | This article considers the problem of statistical classification involving multivariate normal populations and compares the performance of the linear discriminant function (LDF) and the Euclidean distance function (EDF), Although the LDF is quite popular and robust, it has been established (Marco, Young and Turner, 1989) that under certain non-trivial conditions, the EDF is "equivalent" to the LDF, in terms of equal probabilities of misclassifica-tion (error rates). Thus it follows that under those conditions the sample EDF could perform better than the sample LDF, since the sample EDF involves estimation of fewer parameters. Sindation results, also from the above paper; seemed to support this hypothesis. This article compares the two sample discriminant functions through asymptotic expansions of error rates, and identifies situations when the sample EDF should perform better than the sample LDF. Results from simulation experiments are also reported and discussed. |
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Keywords: | linear discriminant function Euclidean distance classifier error rate asymptotic expansion |
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