The consistency for estimator of nonparametric regression model based on NOD errors

By using some inequalities for NOD random variables, we give its application to investigate the nonparametric regression model based on these errors. Some consistency results for the estimator of g ( x ) are presented, including the mean convergence, uniform convergence, almost sure convergence and convergence rate. We generalize some related results and as an example of designed assumptions for weight functions, we give the nearest neighbor weights. AMS Mathematical Subject Classification 2000 : 62G05; 62G08.