# Team : mistis

## Section: Scientific Foundations

Keywords : non parametric, boundary estimation, extremes, wavelets, scaling laws, singularity spectra.

### Functional Inference, semi and non parametric methods

Participants : Charles Bouveyron, Laurent Gardes, Stéphane Girard, Paulo Goncalvès.

We also consider methods which do not assume a parametric model.
Such methods are used for instance to study distribution tails
without introducing a parametric model on the data: this is part
of the *extreme values theory*. Similarly, the grey-levels surface
in an image cannot usually be described through a simple
mathematical equation. Projection methods are then a way to
decompose the unknown signal or image on a set of functions (*e.g.* wavelets). Kernel methods which rely on smoothing the data
using a set of kernels (usually probability distributions), are
other examples. Relationships exist between these methods and
learning techniques using Support Vector Machine (SVM) as this
appears in the context of *boundary estimation*.
As regards wavelets, our goal is to propose wavelet based estimators aimed at
characterizing and analyzing scaling laws structures of processes
or systems. The compression/dilation operator, at the core of
wavelet analysis, allows to identify complex scale organizations,
such as 1/f type processes (e.g.mono-fractals), high order
statistics governed by power laws (e.g. multi-fractals), or more
generally cascade type constructions of measures and processes.