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Biometrika 1990 77(1):227-229;
© 1990 by Biometrika Trust
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MISCELLANEA

Comparison of linear and quadratic discriminant functions

HIROFUMI WAKAKI

Department of Information Science and Systems Engineering, Oita University Oita, 870–11, Japan

Received for publication 1 February 1988. Revision received 1 July 1989.
  Abstract

Asymptotic expansions of the distributions of the linear and the quadratic discriminant functions are derived. The expected misclassification probabilities of these two functions are compared when the covariance matrices are proportional and the sample sizes are equal. Some numerical experiments are carried out to investigate the relation between the parameters and the boundary point such that if the sample size is smaller than the point the linear discriminant function is better than the quadratic discriminant function.

Key Words: Asymptotic expansion • Linear discriminant function • Probability of misclassification • Quadratic discriminant function


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