Bootstrap for the sample mean and for U-Statistics of stationary processes

Abstract

The validity of various bootstrapping methods has been proved for the sample mean of strongly mixing data. But in many applications, there appear nonlinear statistics of processes that are not strongly mixing. We investigate the nonoverlapping block bootstrap for functionals of absolutely regular processes, which occur from chaotic dynamical systems. We establish the strong consistency of the bootstrap distribution estimator not only for the sample mean, but also for U-statistics, which include examples as Gini’s mean difference or the x 2-test statistic. AMS subject classification: 62G09, 60G10.