The Annals of Probability

On the Convergence Rate in the Central Limit Theorem for Associated Processes

Thomas Birkel

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Abstract

We give uniform rates of convergence in the central limit theorem for associated processes with finite third moment. No stationarity is required. Using a coefficient $u(n)$ which describes the covariance structure of the process, we obtain a convergence rate $O(n^{-1/2}\log^2n)$ if $u(n)$ exponentially decreases to 0. An example shows that such a rate can no longer be obtained if $u(n)$ decreases only as a power.

Article information

Source
Ann. Probab., Volume 16, Number 4 (1988), 1685-1698.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991591

Digital Object Identifier
doi:10.1214/aop/1176991591

Mathematical Reviews number (MathSciNet)
MR958210

Zentralblatt MATH identifier
0658.60039

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Keywords
Central limit theorem associated random variables convergence rate

Citation

Birkel, Thomas. On the Convergence Rate in the Central Limit Theorem for Associated Processes. Ann. Probab. 16 (1988), no. 4, 1685--1698. doi:10.1214/aop/1176991591. https://projecteuclid.org/euclid.aop/1176991591


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