On the Number of Bootstrap Repetitions for BCa Confidence Intervals

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.