  When randomized ensemble methods such as bagging and random forests are
implemented, a basic question arises: Is the ensemble large enough? In
particular, the practitioner desires a rigorous guarantee that a given ensemble
will perform nearly as well as an ideal infinite ensemble (trained on the same
data). The purpose of the current paper is to develop a bootstrap method for
solving this problem in the context of regression --- which complements our
companion paper in the context of classification (Lopes 2019). In contrast to
the classification setting, the current paper shows that theoretical guarantees
for the proposed bootstrap can be established under much weaker assumptions. In
addition, we illustrate the flexibility of the method by showing how it can be
adapted to measure algorithmic convergence for variable selection. Lastly, we
provide numerical results demonstrating that the method works well in a range
of situations.
