Complete moment convergence for m-END random variables with application to non-parametric regression models

Abstract

In this paper, we study the complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END) random variables, which generalizes some corresponding ones for complete convergence. We also give an application to non-parametric regression model based on m-END errors by using the complete convergence that we establish. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed. We also provide a numerical simulation to verify the validity of our theoretical result.