Weak transport inequalities and applications to exponential inequalities and oracle inequalities
| Autor: | Wintenberger, Olivier |
|---|---|
| Přispěvatelé: | Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Probability (math.PR)
Mathematics - Statistics Theory Statistics Theory (math.ST) [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ordinary least square estimator [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] concentration of measures time series prediction 60E15 28A35 62J05 62M10 62M20 [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] FOS: Mathematics oracle inequalities weakly dependent time series transport inequalities Mathematics - Probability |
| Zdroj: | Electronic Journal of Probability Electronic Journal of Probability, 2015, 20 (none), ⟨10.1214/EJP.v20-3558⟩ |
| ISSN: | 1083-6489 |
| DOI: | 10.1214/EJP.v20-3558⟩ |
| Popis: | We extend the dimension free Talagrand inequalities for convex distance \cite{talagrand:1995} using an extension of Marton's weak transport \cite{marton:1996a} 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 Poincar\'e inequality \cite{bobkov:gotze:1999a}. We obtain new weak transport inequalities for non products measures extending the results of Samson in \cite{samson:2000}. 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 \cite{djellout:guillin:wu:2004,marton:2004}. 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. |
| Databáze: | OpenAIRE |
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