Bootstrap for the Sample Mean and for U-Statistics of Mixing and Near\n Epoch Dependent Processes

2009/11/16 by Olimjon Sh. Sharipov, Sharipov, Olimjon Sh., Martin Wendler +1
Economics, Econometrics and Finance · Mathematics · #60G10 #62G09 #Advanced Statistical Methods and Models #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.0911.3083

openalex publication_date 2009/11/16 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

The validity of various bootstrapping methods has been proved for the sample\nmean of strongly mixing data. But in many applications, there appear nonlinear\nstatistics of processes that are not strongly mixing. We investigate the\nnonoverlapping block bootstrap sequences which are near epoch dependent on\nstrong mixing or absolutely regular processes. This includes ARMA and\nGARCH-processes as well as data from chaotic dynamical systems. We establish\nthe strong consistency of the bootstrap distribution estimator not only for the\nsample mean, but also for U-statistics, which include examples as Gini's mean\ndifference or the chi²-test statistic.\n

Citations

• Bootstrap Methods: Another Look at the Jackknife

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