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Error rates of non-Bayes classification rules and the robustness of Fisher’s linear discriminant function. (English) Zbl 0754.62047
Summary: 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, $$\hat F$$, and the quadratic discriminant rule, $$\hat Q$$, under departures from the equal variance matrices assumption. It is found that $$\hat F$$ is quite robust to departures from the equal variances assumption.

##### MSC:
 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62E20 Asymptotic distribution theory in statistics 62F15 Bayesian inference
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