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Biometrika 1992 79(1):177-184; doi:10.1093/biomet/79.1.177
© 1992 by Biometrika Trust
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Error rates of non-Bayes classification rules and the robustness of Fisher's linear discriminant function

TERENCE J. O'NEILL

Department of Statistics, Faculty of Economics and Commerce, Australian National University GPO Box 4, Canberra ACT 2601, Australia

We call a classification procedure non-Bayes if it does not converge to the Bayes classification procedure. An asymptotic expansion is found for the expected error rate of such a classification rule. This is used to compare the estimates of Fisher's linear discriminant rule, F, and the quadratic discriminant rule, Q, under departures from the equal variance matrices assumption. It is found that F is quite robust to departures from the equal variances assumption.

Key Words: Error rate • Fisher's linear discriminant rule • Non-Bayes classification rules • Quadratic discriminant rule • Unequal variance matri


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