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The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors

Author

Listed:
  • Xin Deng

    (Chuzhou University)

  • Xuejun Wang

    (Anhui University)

  • Yi Wu

    (Anhui University)

Abstract

In this paper, the Berry–Esseen type bounds of the weighted estimator in a nonparametric regression model are investigated under some mild conditions when random errors are from a linear process generated by $$\varphi $$ φ -mixing random variables. In particular, the rate of uniform normal approximation is near to $$O(n^{-\frac{3}{16}})$$ O ( n - 3 16 ) by the choice of some constants, which generalizes and improves the corresponding results of Li et al. (Stat Probab Lett 81:103–110, 2011) and Ding et al. (J Inequal Appl 2018:10, 2018). Finally, the simulation study is provided to verify the validity of the theoretical results.

Suggested Citation

  • Xin Deng & Xuejun Wang & Yi Wu, 2021. "The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors," Statistical Papers, Springer, vol. 62(2), pages 963-984, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01120-z
    DOI: 10.1007/s00362-019-01120-z
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    References listed on IDEAS

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    1. Aiting Shen & Ying Zhang & Andrei Volodin, 2015. "Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 295-311, April.
    2. Xuejun Wang & Zeyu Si, 2015. "Complete consistency of the estimator of nonparametric regression model under ND sequence," Statistical Papers, Springer, vol. 56(3), pages 585-596, August.
    3. Han-Ying Liang & Deli Li & Tianxuan Miao, 2016. "Berry–Esseen type bound of conditional mode estimation under truncation and strong mixing assumptions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5077-5097, September.
    4. Li, Yongming & Wei, Chengdong & Xing, Guodong, 2011. "Berry-Esseen bounds for wavelet estimator in a regression model with linear process errors," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 103-110, January.
    5. Liang, Han-Ying & Fan, Guo-Liang, 2009. "Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 1-15, January.
    6. Kim, Tae-Sung & Ko, Mi-Hwa, 2008. "Complete moment convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 839-846, May.
    7. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    8. Aiting Shen, 2016. "Complete convergence for weighted sums of END random variables and its application to nonparametric regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 702-715, October.
    9. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
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