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Asymptotic properties of wavelet estimators in partially linear errors-in-variables models with long-memory errors

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Abstract

While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables (EV) model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.

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Acknowledgements

We would like to thank three anonymous referees for constructive comments that led to substantial improvements of the paper. In particular, one anonymous referee puts forward an interesting issue, that is, the measurement errors are also long range dependent random variables or measurable functions of long range dependent random variables. Since it is a difficult problem, we are going to investigate it in the future.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

    Hong-chang Hu & Kai-can Li

  2. School of Mathematical science, Capital Normal University, Beijing, 100048, China

    Heng-jian Cui

Authors
  1. Hong-chang Hu
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  2. Heng-jian Cui
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  3. Kai-can Li
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Correspondence to Hong-chang Hu.

Additional information

Supported by the National Natural Science Foundation of China (No.11471105, 11471223), Scientific Research Item of Education Office, Hubei (No.D20172501).

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Hu, Hc., Cui, Hj. & Li, Kc. Asymptotic properties of wavelet estimators in partially linear errors-in-variables models with long-memory errors. Acta Math. Appl. Sin. Engl. Ser. 34, 77–96 (2018). https://doi.org/10.1007/s10255-018-0730-5

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  • DOI: https://doi.org/10.1007/s10255-018-0730-5

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