Abstract
In this article, based on NQD samples, we investigate the fixed design nonparametric regression model, i.e. Ynk = g(xnk )+ enk for 1 ≤ k ≤ n ,w hereenk are pairwise NQD random errors, xnk are fixed design points, and g(·) is an unknown function. The nonparametric weighted estimator gn(· )o fg(·) 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.
Highlights
1 Introduction In regression analysis, it is a common practice to investigate the functional relationship between the responses and design points
In the article, based on several related lemmas, we investigate the fixed design nonparametric regression model with NQD errors
2.2 Basic assumptions Unless otherwise specified, we assume throughout the paper that the random sample for ≤ k ≤ n come from the regression model
Summary
It is a common practice to investigate the functional relationship between the responses and design points. We shall investigate the above nonparametric regression problem under pairwise NQD errors, which means a more general case for sampling.
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