Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables

Abstract

Abstract For arrays of rowwise pairwise negative quadrant dependent random variables, conditions are provided under which weighted averages converge in mean to 0 thereby extending a result of Chandra, and conditions are also provided under which normed and centered row sums converge in mean to 0. These results are new even if the random variables in each row of the array are independent. Examples are provided showing (i) that the results can fail if the rowwise pairwise negative quadrant dependent hypotheses are dispensed with, and (ii) that almost sure convergence does not necessarily hold.

Keywords

• Array of rowwise pairwise negative quadrant dependent random variables
• Pairwise independent random variables
• Weighted averages
• Degenerate mean convergence
• Stochastic domination
• Almost sure convergence