Complete and complete moment convergence with applications to the EV regression models

In this paper, the complete convergence and complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END, for short) random variables are established. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for m-END random variables is also achieved. By using the results that we established, we further investigate the strong consistency of the least square estimator in the simple linear errors-in-variables models, and provide some simulations to verify the validity of our theoretical results.