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 = ∞. 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.
Andrews, Donald W.K. and Buchinsky, Moshe, "Confidence Intervals" (2000). Cowles Foundation Discussion Papers. 1500.