Displaying similar documents to “Some applications of concentration inequalities to statistics”

High-dimensional gaussian model selection on a gaussian design

Nicolas Verzelen (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the problem of estimating the conditional mean of a real gaussian variable =∑=1 + where the vector of the covariates ( )1≤≤ follows a joint gaussian distribution. This issue often occurs when one aims at estimating the graph or the distribution of a gaussian graphical model. We introduce a general model selection procedure which is based on the minimization of a penalized least squares type criterion....

Adaptive Dantzig density estimation

K. Bertin, E. Le Pennec, V. Rivoirard (2011)

Annales de l'I.H.P. Probabilités et statistiques

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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...