
Paulo Gonçalves Inria senior researcher in the project DANTE A joint team of Inria RhoneAlpes and ENS Lyon (LIP) 
Signal Processing applied to Networks  
TimeFrequency Analysis TimeScale Analysis 

Wavelets and Fractals Wavelets History by I. Daubechies 

Wavelets and Statistics 
Description: Heavy tailed distributions which allow for values
far from the mean to occur with considerable probability are of increasing importance
in various applications as the arsenal of analytical and numerical tools grows.
Examples of interest are the Stable and more generally the Pareto distributions for
which moments of sufficiently large order diverge. In fact, the asymptotic powerlaws
of the distribution function at infinity and zero are directly related to the existence
of positive and negative order moments, respectively. In practice, however, when dealing
with finite size data sets of an unknown distribution, standard empirical estimators of
moments will typically fail to reflect the theoretical divergence of moments and provide
finite estimates for all order moments. The main contribution of this paper is an empirical
waveletbased estimator for the characteristic exponents C+ and C of a random variable,
which bound the interval of all orders r with finite moment Ex^r.
This objective is achieved by deriving a theoretical equivalence between finiteness of
moments and the local H\"older regularity of the characteristic function at the origin and
by deriving a wavelet based estimation scheme which is particularly suited to characteristic functions.
Joint work with: Rudolf Riedi 

Other applications 