Convergence rates in the law of the iterated logarithm for negatively associated random variables with multidimensional indices

For a set of negatively associated random variables indexed by Nd, d≥2, the positive integer d-dimensional lattice points, convergence rates in the law of the iterated logarithm are discussed. Then the results of Gut (see [Gut, A. (1980). Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices. Ann. Probab. 8, 298-313]) are extended.