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Concentration Inequalities - A Nonasymptotic Theory of Independence
Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes. Expand
Concentration inequalities and model selection
Exponential and Information Inequalities.- Gaussian Processes.- Gaussian Model Selection.- Concentration Inequalities.- Maximal Inequalities.- Density Estimation via Model Selection.- StatisticalExpand
Risk bounds for model selection via penalization
Abstract Performance bounds for criteria for model selection are developed using recent theory for sieves. The model selection criteria are based on an empirical loss or contrast function with anExpand
Adaptive estimation of a quadratic functional by model selection
We consider the problem of estimating ∥s∥ 2 when s belongs to some separable Hilbert space and one observes the Gaussian process Y(t) = (s, t) + σ L(t), for all t ∈ H, where L is some GaussianExpand
Gaussian model selection
Abstract.Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage andExpand
Minimal Penalties for Gaussian Model Selection
This paper is mainly devoted to a precise analysis of what kind of penalties should be used in order to perform model selection via the minimization of a penalized least-squares type criterion withinExpand
From Model Selection to Adaptive Estimation
Many different model selection information criteria can be found in the literature in various contexts including regression and density estimation. There is a huge amount of literature concerningExpand
The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality
Let F^ n denote the empirical distribution function for a sample of n i.i.d. random variables with distribution function F. In 1956 Dvoretzky, Kiefer and Wolfowitz proved that P(√n sup x (F^ nExpand
Some applications of concentration inequalities to statistics
Nous presentons quelques applications d'inegalites de concentration a la resolution de problemes de selection de modeles en statistique. Nous etudions en detail deux exemples pour lesquels cetteExpand