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In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on-mixing random errors. The  r -th mean consistency and uniform consistency are established under some suitable conditions. Finally, a simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimators is provided. The results obtained in the paper complement the existing ones of independent random errors to the case of-mixing random errors.

A note on the asymptotic properties of the estimators in a semiparametric regression model