Bootstrapping U-Quantiles

摘要

The asymptotic consistency of the bootstrap approximation for generalizedquantiles of U statistic structure (U quantiles for short) is established. The same method of proof also yields the asymptotic accuracy of the bootstrap approximation in this case. Aplications to location and spread estimators, such as the classical sample quantile, the Hodges-Lehmann estimator of location and a spread estimator proposed by Bickel and Lehmann are given. The method of proof for the asymptotic consistency relies on an idea of Sheehy and Wellner (1988), who treat the sample median.