We give uniform rates of convergence in the central limit theorem for negatively associated random fields with finite (2+[delta])th moment. These results are of an order close to the best possible if not the best possible. As application, we obtain precise asymptotics in the law of the logarithm.

Let {Xn,n[greater-or-equal, slanted]1} be a strictly stationary positively or negatively associated sequence of positive random variables with and . Denote and [gamma]=[sigma]/[mu] the coefficient of variation. Under suitable conditions, we show thatwhere , F(·) is the distribution function...