Statistical estimation for multiplicative cascades

By Mina E. Ossiander, E. Waymire. 2000

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Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology (2013, background): “Ossiander and Waymire (2000) already caution against using high moments in multifractal estimation, but their particular focus is on discrete multiplicative cascade models.”
Scattering Representations for Recognition (2013, methodology): “However, the variance of this estimator converges very slowly with the sample size, as N−1+α with α > 0, as shown in [BKM08b; OW00].”
Multifractal rainfall extremes: Theoretical analysis and practical estimation (2009, background): “For a detailed analysis of the root cause of these phenomena (the fact that high-order singularities are not observable in one-dimensional cascades), see [30, 31].”
Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation (2009, methodology): “[1998] (see their Figure 4) obtained using the iid “β” model proposed by Over and Gupta [1994]. There was only minor improvement in model performance by introducing timescale dependence of the model parameters.”
From Multifractal Measures to Multifractal Wavelet Series (2005, methodology): “Their analysis led to a large literature [38, 37, 27, 19, 47, 7, 6, 50].”