On the complete convergence of weighted sums for arrays of negatively associated variables

We discuss the complete convergence of weighted sums for arrays of row negatively associated (NA) random variables. As an application, we obtain the complete convergence of moving average processes based on NA random variables, which extends the result of Li et al. [Li D., Rao, M. B., Wang, X. C. (1992). Complete convergence of moving average processes. Statistics & Probability Letters, 14, 111–114], including the results of [Baum L. E., Katz, M. (1965). Convergence rates in the law of large numbers. Transactions of the American Mathematical Society, 120, 108–123], from i.i.d. case to NA setting. Also, the results of Ahmed et al. [Ahmed, S. E., Antonini, R. G., Volodin, A. (2002). On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes. Statistics & Probability Letters, 58, 185–194] are complemented, and their conjecture on moving average processes is answered in NA case.