Moment inequalities for $m$-NOD random variables and their applications

The concept of $m$-negatively orthant dependent ($m$-NOD) random variables is introduced, and the moment inequalities for $m$-NOD random variables, especially the Marcinkiewicz–Zygmund-type inequality and Rosenthal-type inequality, are established. As one application of the moment inequalities, we study the $L_r$ convergence and strong convergence for $m$-NOD random variables under some uniformly integrable conditions. On the other hand, the asymptotic approximation of inverse moments for nonnegative $m$-NOD random variables with finite first moments is established. The results obtained in the paper generalize or improve some known ones for independent sequences and some dependent sequences.