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In this paper, some moment inequalities for m -extended negatively dependent (m END, for short) random variables are established which can be applied to investigate the nonparametric regression models based on m -END errors. Some results on mean consistency for the estimator in nonparametric regression models are presented. As an application, the consistency for the nearest neighbor estimator is obtained. Mathematics subject classification (2010): 62G05.

The mean consistency of the weighted estimator in the fixed design regression models based on m-END errors