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Statistical Papers

, Volume 60, Issue 6, pp 2087–2108 | Cite as

The asymptotic properties of the estimators in a semiparametric regression model

  • Xuejun WangEmail author
  • Meimei Ge
  • Yi Wu
Regular Article

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.

Keywords

Semiparametric regression model Complete consistency Mean consistency \(\varphi \)-mixing random variables 

Mathematics Subject Classification

62G05 

Notes

Acknowledgements

The authors are most grateful to the Editor-in-Chief Prof. Christine H. Müller and two anonymous referees for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper. This work was supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06) and the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesAnhui UniversityHefeiPeople’s Republic of China
  2. 2.School of Mathematics and FinanceChuzhou UniversityChuzhouPeople’s Republic of China

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