Adaptive Dantzig density estimation
The aim of this paper is to build an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose a minimization of the 1-norm of the coefficients in the linear combination under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global structure assumptions, oracle inequalities are derived. These theoretical results are transposed...