Heteroscedastic Discriminant Analysis with a Preassigned Misclassification Probability

SYNOPTIC ABSTRACT

We derive an exact expression for the misclassification probability of a classification rule based on the Heteroscedastic Method of Dudewicz and Bishop (1979) (see also Dudewicz and Taneja (1989)), in the case of two univariate normal populations. The procedure guarantees the misclassification probability does not exceed a preassigned bound set by the experimenter. As this bound does not depend on the unknown variances, the experimenter can make requirements such as the following for the first time for any procedure: the misclassification probability should not exceed the best possible by more than .05 when the means of the populations differ by at least 3.5 units.

Key Words and Phrases:

• Characteristic requirement
• discriminant analysis
• heteroscedasticity
• heteroscedastic method
• misclassification probability
• preassigned bound