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

Abstract

In this article, based on NQD samples, we investigate the fixed design nonparametric regression model, i.e. Y nk = g(x nk ) + ε nk for 1 ≤ k ≤ n, where ε nk are pairwise NQD random errors, x nk are fixed design points, and g(·) is an unknown function. The nonparametric weighted estimator g n (·) 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.