MONTE-CARLO APPROXIMATION AND THE ITERATED BOOTSTRAP

We discuss optimal choice of the numbers of resamples in the two stages of the iterated bootstrap, when that technique is used to calibrate bootstrap confidence intervals. If the numbers of resamples in the first and second stages are denoted by B and C respectively, we show that it is optimal to take C to be approximately a constant multiple of B1/2. The value of the constant is derived, and shown to depend only on the nominal coverage level of a confidence interval. However, it assumes different values in the cases of one- and two-sided intervals.