Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables and Its Application in Non-Parametric Regression Model

Abstract

In this paper, some results on the complete moment convergence for arrays of rowwise negatively associated (NA, for short) random variables are established. The results obtained in this paper correct the corresponding one obtained in Ko [13] and also improve and generalize the corresponding ones of Kuczmaszewska [14] and Ko [13]. As an application of the main results, we present a result on complete consistency for the estimator in a non-parametric regression model based on NA errors. Finally, we provide a numerical simulation to verify the validity of our result.

On complete and complete moment convergence for weighted sums of widely orthant dependent random variables

“…It can be easily verified that complete moment convergence implies complete convergence; thus, complete moment convergence is much stronger than complete convergence. For more details about complete moment convergence, one can refer to Liang et al [22], Wu et al [23], Shen et al [24] and Wu et al [25] for instance.…”