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The asymptotic properties of the estimators in a semiparametric regression model. (English) Zbl 1432.62082

Summary: In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on \(\varphi\)-mixing random variables. The \(r\)-th mean consistency, complete consistency, uniform \(r\)-th 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.

MSC:

62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
60F17 Functional limit theorems; invariance principles
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