On convergence properties for weighted sums of coordinatewise ANA random vectors in Hilbert spaces.

In this article, the complete convergence and complete moment convergence for weighted sums of asymptotically negatively associated random vectors are investigated. The results obtained in this article extend the corresponding ones for random variables in Chen et al. to H-valued random vectors. Weighted version of strong law of large numbers and complete integral convergence result are also presented. [ABSTRACT FROM AUTHOR]