Nonparametric estimation of the Bayes risk R^\ast using a k -nearest-neighbor ( k -NN) approach is investigated. Estimates of the conditional Bayes error r(X) for use in an unclassified test sample approach to estimate R^\ast are derived using maximum-likelihood estimation techniques. By using the volume information as well as the class representations of the k -NN's to X , the mean-squared error of the conditional Bayes error estimate is reduced significantly. Simulations are presented to indicate the performance of the estimates using unclassified testing samples.