Computationally Efficient Double Bootstrap Variance Estimation

The double bootstrap provides a useful tool for bootstrapping approximately pivotal quantities by using an "inner" bootstrap loop to estimate the variance. When the estimators are computationally intensive, the double bootstrap may become infeasible. We propose the use of a new variance estimator for the nonparametric bootstrap which effectively removes the requirement to perform the inner loop of the double bootstrap. Simulation results indicate that the proposed estimator produce bootstrap-t confidence intervals with coverage accuracy which replicates the coverage accuracy for the standard double bootstrap.