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Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples

Author

Listed:
  • Liwang Ding

    (Nanjing University of Science and Technology
    Guangxi University of Finance and Economics)

  • Ping Chen

    (Nanjing University of Science and Technology)

  • Yongming Li

    (Shanghai University of Finance and Economics)

Abstract

In this article, we mainly study the consistency properties of wavelet estimator in nonparametric regression model with extended negatively dependent samples. Under some suitable conditions, the pth mean consistency, complete consistency and complete consistency rates of the wavelet estimator in nonparametric regression model with extended negatively dependent samples are obtained. Our results generalize or improve the corresponding ones and the wavelet estimator method for independent and mixing dependent samples to some extent.

Suggested Citation

  • Liwang Ding & Ping Chen & Yongming Li, 2020. "Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples," Statistical Papers, Springer, vol. 61(6), pages 2331-2349, December.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1050-9
    DOI: 10.1007/s00362-018-1050-9
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    References listed on IDEAS

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    1. 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.
    2. Hongchang Hu & Yu Zhang & Xiong Pan, 2016. "Asymptotic normality of DHD estimators in a partially linear model," Statistical Papers, Springer, vol. 57(3), pages 567-587, September.
    3. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.
    4. 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.
    5. Xuejun Wang & Fengxi Xia & Meimei Ge & Shuhe Hu & Wenzhi Yang, 2012. "Complete Consistency of the Estimator of Nonparametric Regression Models Based on -Mixing Sequences," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, December.
    6. Xuejun Wang & Xiaoqin Li & Shuhe Hu & Xinghui Wang, 2014. "On Complete Convergence for an Extended Negatively Dependent Sequence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(14), pages 2923-2937, July.
    7. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    8. Zhou, Xing-cai & Lin, Jin-guan, 2013. "Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 251-270.
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