Estimating Prediction Errors in Binary Classification Problem: Cross-Validation versus Bootstrap

It is important to estimate the true misclassification rate of a given classifier when an independent set of test data is not available. Cross-validation and bootstrap are two possible approaches in this case. In related literature bootstrap estimators of the true misclassification rate were asserted to have better performance for small samples than cross-validation estimators. We compare the two estimators empirically when the classification rule is so adaptive to training data that its apparent misclassification rate is close to zero. We confirm that bootstrap estimators have better performance for small samples because of small variance, and we have found a new fact that their bias tends to be significant even for moderate to large samples, in which case cross-validation estimators have better performance with less computation.