On the Number of Bootstrap Repetitions for Bootstrap Standard Errors, Confidence Intervals, and Tests

This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, and tests. For each of these problems, the paper provides a three-step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval endpoint(s), test's critical value, or test's p-value based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B = infinity. Monte Carlo simulations show that the proposed methods work quite well. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals.