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Asymptotic Normality for Wavelet Estimators in Heteroscedastic Semiparametric Model with Random Errors

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Abstract

For the heteroscedastic regression model Yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n, where σ 2i = f (ui), the design points (xi, ti, ui) are known and nonrandom, g(·) and f(·) are defined on the closed interval [0,1]. When f(·) is known, we investigate the asymptotic normality for wavelet estimators of β and g(·) under {ei, 1 ≤ i ≤ n} is a sequence of identically distributed a-mixing errors; when f(·) is unknown, the asymptotic normality for wavelet estimators of β, g(·) and f(·) are established under independent errors. A simulation study is provided to illustrate the feasibility of the theoretical result that the authors derived.

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Acknowledgements

The authors are grateful to the Editor, associate Editor and two referees for carefully reading the manuscript and for providing helpful comments and constructive criticism which enabled them to improve the paper.

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Liwang Ding, Ping Chen & Qiang Zhang

  2. School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, 530003, China

    Liwang Ding

  3. School of Mathematics and Computer Science, Shangrao Normal University, Shangrao, 334001, China

    Yongming Li

Authors
  1. Liwang Ding
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  2. Ping Chen
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  3. Qiang Zhang
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  4. Yongming Li
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Corresponding author

Correspondence to Liwang Ding.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11271189, 11461057, Science Foundation of Guangxi Education Department under Grant No. 2019KY0646 and 2019 Youth Teacher Research, the Development Fund Project of Guangxi University of Finance and Economics under Grant No. 2019QNB07, and the Discipline Project of School of Information and Statistics of Guangxi University of Finance and Economics under Grant No. 2019XTZZ07.

This paper was recommended for publication by Editor DONG Yuexiao.

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Ding, L., Chen, P., Zhang, Q. et al. Asymptotic Normality for Wavelet Estimators in Heteroscedastic Semiparametric Model with Random Errors. J Syst Sci Complex 33, 1212–1243 (2020). https://doi.org/10.1007/s11424-020-8210-4

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  • DOI: https://doi.org/10.1007/s11424-020-8210-4

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