Inria senior researcher in the project DANTE
A joint team of Inria Rhone-Alpes and ENS Lyon (LIP)
|Signal Processing applied to Networks|
Wavelets and Fractals
by I. Daubechies
|Wavelets and Statistics||
Description: Stable distributions are characterized by four parameters which can
be estimated via a number of methods, and although approximate maximum likelihood estimation
techniques have been proposed, they are computationally intensive and difficult to implement.
This article describes a fast, wavelet-based, regression-type method for estimating the
parameters of a stable distribution. Fourier domain representations, combined with a wavelet
multiresolution approach, are shown to be effective and highly efficient tools for inference
in stable law families. Our procedures are illustrated and compared with other estimation methods
using simulated data from stable distributions and an application to a real data example is explored.
One novel aspect of this work is that here wavelets are being used to solve a parametric problem
rather than a nonparametric one, which is the more typical context in wavelet applications.
Joint work with: Anestis Antoniadis (INPG-IMAG), Andrey Feuerverger (Univ. of Toronto)