The validity of various bootstrapping methods has been proved for the samplemean of strongly mixing data. But in many applications, there appear nonlinearstatistics of processes that are not strongly mixing. We investigate thenonoverlapping block bootstrap sequences which are near epoch dependent onstrong mixing or absolutely regular processes. This includes ARMA andGARCH-processes as well as data from chaotic dynamical systems. We establishthe strong consistency of the bootstrap distribution estimator not only for thesample mean, but also for U-statistics, which include examples as Gini's meandifference or the chi^2-test statistic.
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