On the consistency of the P–C estimator in a nonparametric regression model

In this paper, we investigate the nonparametric regression model based on extended negatively dependent errors. Some consistency results for the estimator of the regression function g(x) are presented, including the rates of strong consistency and complete consistency, and the mean convergence. The results obtained in this paper improve and extend the corresponding ones of Yang and Wang (Acta Math Appl Sin 22(4):522–530, 1999) and Priestley and Chao (J R Stat Soc B 34:385–392, 1972). Finally, we present a numerical simulation study to verify the validity of the results established here.