Abstract
In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on $$\varphi $$ -mixing random variables. The rth mean consistency, complete consistency, uniform rth mean consistency and uniform complete consistency are established under some suitable conditions. In addition, a simulation to study the numerical performance of the consistency of the nearest neighbor weight function estimators is provided. The results obtained in the paper improve the conditions in the literature and generalize the existing results of independent random errors to the case of $$\varphi $$ -mixing random errors.
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