The consistency for the estimator of nonparametric regression model based on martingale difference errors

Abstract In this paper, by using the inequalities for martingale difference sequence, we investigate the consistency for the estimator of nonparametric regression model based on martingale difference errors. Some results on consistency for the estimator of $$g(x)$$ g ( x ) are presented, including the mean consistency, complete consistency and strong consistency. As an application, the consistency for the nearest neighbor estimator is obtained.