On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables

Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise negatively orthant dependent random variables. Some sufficient conditions for strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables are presented without the assumption of identical distribution. Our results not only generalize the result of Sung (On the strong convergence for weighted sums of random variables. Stat. Pap. 52: 447–454, 2011) for negatively associated random variables to the case of negatively orthant dependent random variables, but also generalize the result of Sung (Stat. Pap. 52: 447–454, 2011) for 0 < α ≤ 2 to the case of 2 < α < 4.