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

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems

Minimal and ideal distances rates of convergence Martingale difference sequences

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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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