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The asymptotic properties of the estimators in a semiparametric regression model

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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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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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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Xuejun Wang & Yi Wu

  2. School of Mathematics and Finance, Chuzhou University, Chuzhou, 239000, People’s Republic of China

    Meimei Ge

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  1. Xuejun Wang
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  2. Meimei Ge
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  3. Yi Wu
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Correspondence to Xuejun Wang.

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Wang, X., Ge, M. & Wu, Y. The asymptotic properties of the estimators in a semiparametric regression model. Stat Papers 60, 2087–2108 (2019). https://doi.org/10.1007/s00362-017-0910-z

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