An improved version of a result of Chandra, Li, and Rosalsky

Abstract

Abstract For an array of rowwise pairwise negative quadrant dependent, mean 0 random variables, Chandra, Li, and Rosalsky provided conditions under which weighted averages converge in L1 $\mathscr{L}_{1}$ to 0. The Chandra, Li, and Rosalsky result is extended to Lr $\mathscr{L}_{r}$ convergence ( 1≤r<2 $1\leq r<2$) and is shown to hold under weaker conditions by applying a mean convergence result of Sung and an inequality of Adler, Rosalsky, and Taylor.

Keywords

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