Error rates in quadratic discrimination with constraints on the covariance matrices |
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Authors: | Bernhard W. Flury Martin J. Schmid A. Narayanan |
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Affiliation: | (1) Present address: Department of Mathematics, Indiana University, 47405 Bloomington, IN, USA;(2) Present address: Bundesamt für Sozialversicherung, 3000 Bern, Switzerland;(3) Present address: Ivorydale Technical Center, The Procter & Gamble Company, 45217 Cincinnati, Ohio, USA |
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Abstract: | In multivariate discrimination of several normal populations, the optimal classification procedure is based on quadratic discriminant functions. We compare expected error rates of the quadratic classification procedure if the covariance matrices are estimated under the following four models: (i) arbitrary covariance matrices, (ii) common principal components, (iii) proportional covariance matrices, and (iv) identical covariance matrices. Using Monte Carlo simulation to estimate expected error rates, we study the performance of the four discrimination procedures for five different parameter setups corresponding to standard situations that have been used in the literature. The procedures are examined for sample sizes ranging from 10 to 60, and for two to four groups. Our results quantify the extent to which a parsimonious method reduces error rates, and demonstrate that choosing a simple method of discrimination is often beneficial even if the underlying model assumptions are wrong.The authors wish to thank the editor and three referees for their helpful comments on the first draft of this article. M. J. Schmid supported by grants no. 2.724-0.85 and 2.038-0.86 of the Swiss National Science Foundation. |
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Keywords: | Common principal components Linear Discriminant Function Monte Carlo Simulation Proportional Covariance Matrices |
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