On the number of bootstrap repetitions for BCa confidence intervals

This paper considers the problem of choosing the number of bootstrap repetitions B to use with the BC,, bootstrap confidence intervals introduced by Efron (1987, Journal of the American Statistical Association 82, 171-200). 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 = infinity. We specify 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.