Confidence intervals for the random forest generalization error

We show that underneath the training process of a random forest there lies not only the well known and almost computationally free out-of-bag point estimate of its generalization error, but also a path to compute a confidence interval for the generalization error which does not demand a retraining of the forest or any forms of data splitting. Besides the low computational cost involved in its construction, this confidence interval is shown through simulations to have good coverage and appropriate shrinking rate of its width in terms of the training sample size.