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

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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.

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Acknowledgements

The authors are most grateful to the Editor-in-Chief and anonymous referees for a careful reading of the manuscript and for making valuable suggestions which helped in improving an earlier version of this paper. This work was supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06) and The Key Projects for Academic Talent of Anhui Province (gxbjZD2016005).

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Yi Wu & Xuejun Wang

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Narayanaswamy Balakrishnan

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  1. Yi Wu
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  2. Xuejun Wang
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  3. Narayanaswamy Balakrishnan
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Correspondence to Xuejun Wang.

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Wu, Y., Wang, X. & Balakrishnan, N. On the consistency of the P–C estimator in a nonparametric regression model. Stat Papers 61, 899–915 (2020). https://doi.org/10.1007/s00362-017-0966-9

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  • DOI: https://doi.org/10.1007/s00362-017-0966-9

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