Weak transport inequalities and applications to exponential and oracle inequalities
Wintenberger, Olivier (2015), Weak transport inequalities and applications to exponential and oracle inequalities, Electronic Journal of Probability, 20, p. 27 p.. 10.1214/EJP.v20-3558
TypeArticle accepté pour publication ou publié
External document linkhttp://dx.doi.org/10.1214/EJP.v20-3558
Journal nameElectronic Journal of Probability
Electronic Journal of Probability and Electronic Communications in Probability
MetadataShow full item record
Abstract (EN)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.
Subjects / Keywordsoracle inequalities; ordinary least square estimator; weakly dependent time series; concentration of measures; transport inequalities; time series prediction
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