Complete convergence and complete moment convergence for maximal weighted sums of arrays of rowwise extended negatively dependent random variables with statistical applications

In this paper, complete convergence and complete moment convergence for maximal weighted sums of arrays of rowwise extended negatively dependent random variables are investigated, and some sufficient conditions for convergence are provided. Three ways of optimising the conditions for convergence, namely reducing the moment condition, narrowing the boundary function, and raising the weight function respectively, are considered under light weights. Besides, rather than assuming stochastic domination, we turn to a weaker assumption of uniformly bounded expectations to describe the moment conditions. The results obtained in the paper extend the corresponding ones for independent random variables and some dependent random variables. In addition, the results are applied to establish strong consistency for estimators in some statistical models.