The Relationship in Terms of Asymptotic Mean Square Error Between the Separate Problems of Estimating each of the Three Types of Error Rate of the Linear Discriminant Function

Abstract

The problem is to investigate the relationship between the separate problems of estimating each of the three types of error rate (optimal, expected, and conditional) associated with the linear discriminant function. For a general estimator having a form common to that of the majority estimators available in practice, the asymptotic mean square error (AMSE) is derived with respect to each of the three types of error rate. The relationship is then studied in terms of the general expressions for the AMSE.