In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.
Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.
