In this paper, the complete consistency for the weighted estimator of non-parametric regression model based on widely orthant-dependent errors is established, where the restriction imposed on the dominating coefficient g(n) is very general. Moreover, under some stronger moment condition, we further obtain the convergence rate of the complete consistency, where the assumption on the dominating coefficient g(n) is also very general.

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.

Under some mild conditions, the strong consistency and complete consistency of the LS estimators in the errors-in-variable regression model with weakly negative dependent errors are obtained, which generalize the corresponding ones for negatively associated random variables. In addition, the simulation study shows that the biases of our method are small, and our method performs well.