Bootstrap for empirical multifractal analysis

Non-parametric bootstrap approaches can be demonstrated on the analysis of the multifractal properties of empirical hydrodynamic turbulence data. Meanwhile, the concept of scaling has been used for the physical understanding of the mechanisms producing the data or fo standard signal processing tasks such as detection, identification or classification. However, there are inherent difficulties with scaling. Therefore, the use of nonstandard statistical techniques such as bootstrap are handy. For instance, where the models underlying the analyzed data besides their possessing some form of scale invariance is no known, nonparametric bootstrap is used to compensate for that challenge. Nonparametric bootstrap makes use of the empirical distribution, obtained from the available sample to approximate the unknown population distribution which is then used to estimate the distribution of the targeted population parameters. In addition, the empirical distributions of the bootstrap structure functions can be used to construct confidence limits for the structure functions similar to confidence limits for the estimates themselves. Using bootstraps enhance statistical performance and provide satisfactory confidence limits and hypothesis test values for multifractal parameters. It also enables an empirical multifractal analysis toolbox enabling the estimation of multifractal attributes, provide confidence intervals and assess the multifractal properties of real-world empirical data.