On mean central limit theorems for stationary sequences

Jérôme Dedecker; Emmanuel Rio

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 4, page 693-726
  • ISSN: 0246-0203

Abstract

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In this paper, we give estimates of the minimal 𝕃 1 distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.

How to cite

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Dedecker, Jérôme, and Rio, Emmanuel. "On mean central limit theorems for stationary sequences." Annales de l'I.H.P. Probabilités et statistiques 44.4 (2008): 693-726. <http://eudml.org/doc/77988>.

@article{Dedecker2008,
abstract = {In this paper, we give estimates of the minimal $\{\mathbb \{L\}\}^\{1\}$ distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.},
author = {Dedecker, Jérôme, Rio, Emmanuel},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {mean central limit theorem; Wasserstein distance; minimal distance; martingale difference sequences; strong mixing; stationary sequences; weak dependence; rates of convergence; projective criteria},
language = {eng},
number = {4},
pages = {693-726},
publisher = {Gauthier-Villars},
title = {On mean central limit theorems for stationary sequences},
url = {http://eudml.org/doc/77988},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Dedecker, Jérôme
AU - Rio, Emmanuel
TI - On mean central limit theorems for stationary sequences
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 4
SP - 693
EP - 726
AB - In this paper, we give estimates of the minimal ${\mathbb {L}}^{1}$ distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.
LA - eng
KW - mean central limit theorem; Wasserstein distance; minimal distance; martingale difference sequences; strong mixing; stationary sequences; weak dependence; rates of convergence; projective criteria
UR - http://eudml.org/doc/77988
ER -

References

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Citations in EuDML Documents

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  1. J. Dedecker, S. Gouëzel, F. Merlevède, Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains
  2. Jérôme Dedecker, Florence Merlevède, Magda Peligrad, Sergey Utev, Moderate deviations for stationary sequences of bounded random variables
  3. Loïc Hervé, Vitesse de convergence dans le théorème limite central pour des chaînes de Markov fortement ergodiques
  4. Loïc Hervé, Françoise Pène, The Nagaev-Guivarc’h method via the Keller-Liverani theorem

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