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首页> 外文期刊>Journal of nonparametric statistics >Bootstrap for the sample mean and for U-statistics of mixing and near-epoch dependent processes
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Bootstrap for the sample mean and for U-statistics of mixing and near-epoch dependent processes

机译：样本均值以及混合和近似周期依赖过程的U统计量的自举

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摘要

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 x~2-test statistic.
机译：对于强混合数据的样本均值，已证明了各种自举方法的有效性。但是在许多应用中，会出现过程混合程度不高的非线性统计信息。我们研究了非重叠的块引导程序序列，这些序列在很强的混合或绝对有规律的过程中取决于时间。这包括线性过程和条件异方差过程，以及来自混沌动力学系统的数据。我们不仅建立了样本均值的自举分布估计量的强一致性，而且还建立了U统计量（包括吉尼氏均值差或x〜2检验统计量）的自洽分布。

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