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Project

Model selection theory for tree-structured estimation schemes.

The main object of this research are signals, images,. . . that are observed with noise. Once the object of interest can be described in a parsimonious way by a projection onto a family of mathematically well defined atoms (waveforms, bases,. . . ), the denoising or smoothing problem can be interpreted as a model selection problem in the domain of the projection coefficients. Of the currently existing selection rules, a vast majority solely exploits the information given by an individual coefficient. None of the existing approaches addresses the challenge of linking the geometrical structure in the coefficient domain to the development of a functional model on the decay properties of the coefficients over the different scales. We propose to step away from the traditional Besov constraint in order to refine the minimax approach. Also maxiset properties will be studied. Extensions include structures that are no longer trees, such as graphical models. We will extend model selection methods by pooling information and will study the statistical properties of model averaging estimators in this framework.
Date:1 Jan 2012 →  31 Dec 2015
Keywords:Model selection theory, Wavelets, Nonparametric estimation
Disciplines:Applied economics, Economic history, Macroeconomics and monetary economics, Microeconomics, Tourism