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2015 Weak transport inequalities and applications to exponential and oracle inequalities
Olivier Wintenberger
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Electron. J. Probab. 20: 1-27 (2015). DOI: 10.1214/EJP.v20-3558

Abstract

We extend the dimension free Talagrand inequalities for convex distance using an extension of Marton’s weak transport to other metrics than the Hamming distance. We study the dual form of these weak transport inequalities for the euclidian norm and prove that it implies sub-gaussianity and convex Poincaré inequality. We obtain new weak transport inequalities for non products measures extending the results of Samson. Many examples are provided to show that the euclidian norm is an appropriate metric for classical time series. Our approach, based on trajectories coupling, is more efficient to obtain dimension free concentration than existing contractive assumptions. Expressing the concentration properties of the ordinary least square estimator as a conditional weak transport problem, we derive new oracle inequalities with fast rates of convergence in dependent settings.

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Olivier Wintenberger. "Weak transport inequalities and applications to exponential and oracle inequalities." Electron. J. Probab. 20 1 - 27, 2015. https://doi.org/10.1214/EJP.v20-3558

Information

Accepted: 29 October 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1328.60057
MathSciNet: MR3418546
Digital Object Identifier: 10.1214/EJP.v20-3558

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