Nonparametric tolerance intervals for effective bootstrap estimation

A method that allows accurate control of the coverage error in Monte Carlo-approximation of quintiles of the bootstrap distribution is discussed. The method is based on Nonparametric Tolerance Intervals and hence is applicable regardless of the underlying distribution. The results are useful for quantile estimation as well as for construction of robust confidence intervals and interval estimates. The minimum number of bootstrap replicates needed to estimate quantiles to a prescribed conditional coverage accuracy is determined. The results allow the user to perform bootstrap inference without being subject to intolerable fluctuations from Monte Carlo error.