Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model

In this paper, some results on the complete moment convergence for weighted sums of weakly dependent (or ρ∗-mixing) random variables are established. The results obtained in this paper improve and extend the corresponding one of Sung (2010). As an application of the main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on ρ∗-mixing errors.