Bootstrap for the sample mean and for<i>U</i>-statistics of mixing and near-epoch dependent processes
Olimjon Sh. SharipovInstitute of Mathematics and Information Technologies, Uzbek Academy of Sciences , 29 Dormon Yoli Str., Tashkent , 100125 , UzbekistanMartin WendlerFakultät für Mathematik , Ruhr-Universität Bochum , 44780 , Bochum , Germany
ABI
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 sequences which are near-epoch dependent on strong mixing or absolutely regular processes. This includes linear processes and conditional heteroskedastic processes as well as data 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 such examples as Gini's mean difference or the χ2-test statistic.