The consistency of estimator under fixed design regression model with NQD errors

In this article, based on NQD samples, we investigate the fixed design nonparametric regression model, i.e.Ynk=g(xnk)+εnk for 1≤k≤n, where εnk are pairwise NQD random errors, xnk are fixed design points, and g(⋅) is an unknown function. The nonparametric weighted estimator gn(⋅) of g(⋅) will be introduced and its consistency is studied. As a special case, the consistency result for weighted kernel estimators of the model is established. This extends the earlier work on independent random and dependent random errors to the NQD case.