HAL : hal-00719729, version 2

arXiv : 1207.4951

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v1 (20-07-2012)

v2 (09-11-2012)

Weak transport inequalities and applications to exponential inequalities and oracle inequalities

Olivier Wintenberger 1, 2

(20/07/2012)

We extend the weak transport as defined by Marton in \cite{marton:1996a} to other metrics than the Hamming distance. 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 many classical time series. The dual form of the weak transport inequalities yield new exponential inequalities and extensions to the dependent case of the classical result of Talagrand \cite{talagrand:1995} for convex functions that are Lipschitz continuous. Expressing the concentration properties of the ordinary least square estimator as a conditional weak transport problem, we derive from the weak transport inequalities new oracle inequalities with fast rates of convergence.

1 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine
2 :	Laboratoire de Finance Assurance (LFA)
	Centre de Recherche en Économie et STatistique (CREST)

Domaine

:

Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : transport inequalities – concentration of measures – weakly dependent time series – oracle inequalities – ordinary least square estimator – time series prediction.

hal-00719729, version 2

http://hal.archives-ouvertes.fr/hal-00719729

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Contributeur : Olivier Wintenberger <>

Soumis le : Jeudi 8 Novembre 2012, 18:18:46

Dernière modification le : Vendredi 9 Novembre 2012, 08:21:57