Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary α-dependent sequences - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bernoulli Année : 2017

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary α-dependent sequences

Résumé

We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary α-dependent sequences. We prove some moments inequalities of order p for any p ≥ 1, and we give some conditions under which the central limit theorem holds. We apply our results to unbounded functions of expanding maps of the interval with a neutral fixed point at zero. The moment inequalities for the Wasserstein distance are similar to the well known von Bahr-Esseen or Rosenthal bounds for partial sums, and seem to be new even in the case of independent and identically distributed random variables.
Fichier principal
Vignette du fichier
W1CLTmoment.pdf (406.7 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01121156 , version 1 (27-02-2015)

Identifiants

Citer

Jérôme Dedecker, Florence Merlevède. Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary α-dependent sequences. Bernoulli, 2017, pp.2083-2127. ⟨hal-01121156⟩
79 Consultations
1545 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More