Lp $L_{p}$-convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in Rd $\mathbb{R}^{d}$

Abstract

Abstract In this paper, based on the Rosenthal-type inequality for asymptotically negatively associated random vectors with values in Rd $\mathbb{R}^{d}$, we establish results on Lp $L_{p}$-convergence and complete convergence of the maximums of partial sums are established. We also obtain weak laws of large numbers for coordinatewise asymptotically negatively associated random vectors with values in Rd $\mathbb{R}^{d}$.

Keywords

• Asymptotically negative association
• Random vectors
• Rosenthal-type inequality
• L p $L_{p}$ -convergence
• Complete convergence
• Weak laws of large numbers