Electronic Journal of Probability

Rates of convergence for minimal distances in the central limit theorem under projective criteria

Jérôme Dedecker, Florence Merlevède, and Emmanuel Rio

Full-text: Open access

Abstract

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 35, 978-1011.

Dates
Accepted: 12 May 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819496

Digital Object Identifier
doi:10.1214/EJP.v14-648

Mathematical Reviews number (MathSciNet)
MR2506123

Zentralblatt MATH identifier
1191.60025

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

Keywords
Minimal and ideal distances rates of convergence Martingale difference sequences

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Dedecker, Jérôme; Merlevède, Florence; Rio, Emmanuel. Rates of convergence for minimal distances in the central limit theorem under projective criteria. Electron. J. Probab. 14 (2009), paper no. 35, 978--1011. doi:10.1214/EJP.v14-648. https://projecteuclid.org/euclid.ejp/1464819496


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