An Asymptotic Expansion of the Expectation of the Estimated Error Rate in Discriminant Analysis1

Summary When a sample discriminant function is computed, it is desired to estimate the error rate using this function. This is often done by computing G(‐D/2), where G is the cumulative normal distribution and D2 is the estimated Mahalanobis' distance. In this paper an asymptotic expansion of the expectation of G(‐D/2) is derived and is compared with existing Monte Carlo estimates. The asymptotic bias of G(‐D/2) is derived also and the well‐known practical result that G(‐D/2) gives too favourable an estimate of the true error rate