This paper considers the problem of choosing the number bootstrap repetitions B to use with the BCa bootstrap confidence intervals introduced by Efron (1987). Because the simulated random variables are ancillary, we seek a choice of B that yields a confidence interval that is close to the ideal bootstrap confidence interval for which B = ∞. We specifiy a three-step method of choosing B that ensures that the lower and upper lengths of the confidence interval deviate from those of the ideal bootstrap confidence interval by at most a small percentage with high probability.
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 = ∞. 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