Bootstrap for empirical multifractal analysis
Bootstrap for empirical multifractal analysis
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DOI：
10.1109/msp.2007.4286563
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发表时间：
2007-07-01
影响因子：
14.9
通讯作者：
Jaffard, Stephane
中科院分区：
文献类型：
--
作者：
Wendt, Herwig;Abry, Patrice;Jaffard, Stephane
多重分形分析正在成为一种标准的统计分析技术。在信号处理中，它主要包括估计表征标度不变性的标度指数。在实际应用中，估计中的置信区间和假设检验中的p值是最重要的。在经验多重分形分析中，由于多重分形过程的理论性质，估计或检验程序的统计性能仍然超出分析推导。因此，本文的目标是展示非参数自举方法如何规避这些限制，并产生具有令人满意的统计性能的程序，因此可以实际用于现实生活中的数据。这些工具说明在工作中的经验流体动力学湍流数据的多重分形特性的分析。
Multifractal analysis is becoming a standard statistical analysis technique. In signal processing, it mostly consists of estimating scaling exponents characterizing scale invariance properties. For practical purposes, confidence intervals in estimation and p values in hypothesis testing are of primary importance. In empirical multifractal analysis, the statistical performance of estimation or test procedures remain beyond analytical derivation because of the theoretically involved nature of multifractal processes. Therefore, the goal of this article is to show how non-parametric bootstrap approaches circumvent such limitations and yield procedures that exhibit satisfactory statistical performance and can hence be practically used on real-life data. Such tools are illustrated at work on the analysis of the multifractal properties of empirical hydrodynamic turbulence data.