Bootstrapping the distance between smooth bootstrap and sample quantile distribution (Q1112505)

The normalized Kolmogorov-Smirnov and variational distance between the distribution of the sample q-quantile and the pertaining smooth bootstrap distribution are asymptotically distributed like the absolute value of a normal random variable. The distribution functions of these random distances may serve as measures of the accuracy of the bootstrap procedure. It is shown that these distribution functions of random distances, and thus the accuracy of the bootstrap procedure, can again consistently be estimated by means of the bootstrap technique.