Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

On mean central limit theorems for stationary sequences

Jérôme Dedecker and Emmanuel Rio

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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.

Résumé

Dans cet article, nous donnons des majorations de la distance minimale ${\mathbb{L}}^{1}$ entre la loi de la somme normalisée et sa loi limite gaussienne pour des suites stationnaires satisfaisant des critères projectifs à la Gordin ou des conditions de dépendance faible.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 4 (2008), 693-726.

Dates
First available in Project Euclid: 5 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1217964116

Digital Object Identifier
doi:10.1214/07-AIHP117

Mathematical Reviews number (MathSciNet)
MR2446294

Zentralblatt MATH identifier
1187.60015

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Mean central limit theorem Wasserstein distance Minimal distance Martingale difference sequences Strong mixing Stationary sequences Weak dependence Rates of convergence Projective criteria

Citation

Dedecker, Jérôme; Rio, Emmanuel. On mean central limit theorems for stationary sequences. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 4, 693--726. doi:10.1214/07-AIHP117. https://projecteuclid.org/euclid.aihp/1217964116


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