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

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.