The bias of the apparent error rate in discriminant analysis

The apparent error rate is a commonly used estimator of the actual error rate in discriminant analysis. In this study the asymptotic bias of the apparent error rate is derived in the context of two multivariate normal populations with unknown different means and unknown common covariance matrix. From the derived expansion a correction term ia available for reducing the bias of the apparent error rate from the first to the second order with respect to the reciprocals of the initial sample sizes. Also, some previously unanswered questions on inequalities between the average apparent, the optimal, and the average actual error rates are solved.