On the Number of Bootstrap Repetitions for BC_a Confidence Intervals

Abstract

This paper considers the problem of choosing the number bootstrap repetitions B to use with the BC_{a} 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 = infinity. 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.