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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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