| Paper: | SPTM-L5.6 | ||
| Session: | Signal Parameter Estimation | ||
| Time: | Wednesday, May 19, 17:10 - 17:30 | ||
| Presentation: | Lecture | ||
| Topic: | Signal Processing Theory and Methods: Detection, Estimation, and Class. Thry & Apps. | ||
| Title: | SCALING EXPONENTS ESTIMATION FOR MULTISCALING PROCESSES | ||
| Authors: | Bruno Lashermes; École Normale Supérieuré | ||
| Patrice Abry; École Normale Supérieuré | |||
| Pierre Chainais; Université Blaise Pascal | |||
| Abstract: | We study the statistical performance of multiresolution (wavelet based) estimators commonly used for the estimation of the scaling exponents $\zeta(q)$ of multifractal processes. So far, such studies were conducted exclusively using the celebrated Mandelbrot's cascades. A new class of processes, compound Poisson cascades, with better statistical properties --- stationary increments and continuous scale invariance --- has recently been proposed in the literature. Making use of this new type of processes, we show that the multiresolution estimators are characterised by a generic and systematic feature: beyond a critical order $q$ (which is determined analytically), they fail to estimate the $\zeta(q)$ and present instead a linear behaviour in $q$. We study in detail this linearisation effect and show that it does not disappear in the limit of infinite observation duration $n$ and that the parameters characterising it do not depend on $n$. We comment on its major practical consequences and on its having been mostly overlooked in applications. | ||
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