Preprint

Bootstrap for the Sample Mean and for U-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

arXiv (Cornell University)repository2009en

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 ARMA and GARCH-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 examples as Gini's mean difference or the chi^2-test statistic.

Topics

Financial Risk and Volatility Modeling Complex Systems and Time Series Analysis Advanced Statistical Methods and Models

Identifiers

DOI: 10.48550/arxiv.0911.3083

Citations and references

Cited by 018 references

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