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Optimal discriminant functions for normal populations

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  • Wakaki, Hirofumi
  • Aoshima, Makoto

Abstract

A class of discriminant rules which includes Fisher's linear discriminant function and the likelihood ratio criterion is defined. Using asymptotic expansions of the distributions of the discriminant functions in this class, we derive a formula for cut-off points which satisfy some conditions on misclassification probabilities, and derive the optimal rules for some criteria. Some numerical experiments are carried out to examine the performance of the optimal rules for finite numbers of samples.

Suggested Citation

  • Wakaki, Hirofumi & Aoshima, Makoto, 2009. "Optimal discriminant functions for normal populations," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 58-69, January.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:58-69
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    References listed on IDEAS

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    1. T. Anderson, 1951. "Classification by multivariate analysis," Psychometrika, Springer;The Psychometric Society, vol. 16(1), pages 31-50, March.
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