Nonparametric confidence intervals based on extreme bootstrap percentiles

Monte Carlo approximation of standard bootstrap confidence intervals relies on the drawing of a large number, B say, of bootstrap resamples. Conventional choice of B is often made on the order of 1,000. While this choice may prove to be more than sufficient for some cases, it may be far from adequate for others. A new approach is suggested to construct confidence intervals based on extreme bootstrap percentiles and an adaptive choice of B. It economizes on the computational effort in a problem-specific fashion, yielding stable confidence intervals of satisfactory coverage accuracy.