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On the consistency of the P–C estimator in a nonparametric regression model

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  • Yi Wu

    (Anhui University)

  • Xuejun Wang

    (Anhui University)

  • Narayanaswamy Balakrishnan

    (McMaster University)

Abstract

In this paper, we investigate the nonparametric regression model based on extended negatively dependent errors. Some consistency results for the estimator of the regression function g(x) are presented, including the rates of strong consistency and complete consistency, and the mean convergence. The results obtained in this paper improve and extend the corresponding ones of Yang and Wang (Acta Math Appl Sin 22(4):522–530, 1999) and Priestley and Chao (J R Stat Soc B 34:385–392, 1972). Finally, we present a numerical simulation study to verify the validity of the results established here.

Suggested Citation

  • Yi Wu & Xuejun Wang & Narayanaswamy Balakrishnan, 2020. "On the consistency of the P–C estimator in a nonparametric regression model," Statistical Papers, Springer, vol. 61(2), pages 899-915, April.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0966-9
    DOI: 10.1007/s00362-017-0966-9
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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 & 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.
    3. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
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