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On the Convergence Rate in the Central Limit Theorem for Associated Processes
The Annals of Probability
Vol. 16, No. 4 (Oct., 1988), pp. 1685-1698
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243986
Page Count: 14
You can always find the topics here!Topics: Random variables, Central limit theorem, Perceptron convergence procedure, Mathematical inequalities
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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-1/2log2n) 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.
The Annals of Probability © 1988 Institute of Mathematical Statistics