Discriminant analysis when the classes arise from a continuum

Abstract Sometimes two class linear discriminant analysis is applied to situations in which the classes are formed by partitioning an underlying continuum. In such cases, a reasonable assumption is that the underlying continuous “response” variable forms a joint multivariate normal distribution with the predictors. We compare the error rate of linear discriminant analysis with that of the optimal classification rule under these conditions, showing that linear discriminant analysis leads to a decision surface parallel to, but shifted from, the decision surface of the optimal rule and that the two rules can lead to very different error rates.

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