Complete Moment Convergence for Weighted Sums of Negatively Orthant Dependent Random Variables

Abstract

In this paper, the complete moment
convergence and the integrability of the supremum for weighted sums
of negatively orthant dependent (NOD) random variables are
presented. As applications, the complete convergence and the
Marcinkiewicz-Zymund-type strong law of large numbers for NOD random
variables are obtained. The results established in the paper
generalize some corresponding ones for independent random variables
and negatively associated random variables.