Generalized bootstrap for studentized U-statistics: a rank statistic approach

Abstract

The notion of generalized bootstrapping is introduced in Mason and Newton (1992). The study the consistency of generalized bootstrapped means. We extend the validity of the generalized bootstrap to the case of U-statistics and studentized U-statistics. From the proofs it will become clear that the rank statistic methodology is a powerful tool that provides a unified approach to handle different resampling schemes