Asymptotic expansions for the means and variances of error rates

Abstract

The problem of classifying an observation X into one of k multivariate normal distributions is considered. When samples are used to estimate the population parameters, the probabilities of correct classification, and the associated error rates, are random variables. Asymptotic expansions for the expected values and variances of these random variables, in terms of the inverses of the sample sizes, are found. Simulations have been performed to evaluate the expansions.