Two nonparametric methods to estimate the Bayes risk using classified sample sets are described and compared. The first method uses the nearest neighbor error rate as an estimate to bound the Bayes risk. The second method estimates the Bayes decision regions by applying Parzen probability-density function estimates and counts errors made using these regions. This estimate is shown to be asymptotically consistent in mean square. The results of experiments with these estimators on simulated and empirical data imply that the estimators both have acceptable small-sample properties; however, small-sample convergence of both estimators depends strongly on the choice of metric and local area or window size in the measurement space.