IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i2d10.1007_s00362-017-0966-9.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0966-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00362-017-0966-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xuejun Wang & Yi Wu & Shuhe Hu, 2016. "Exponential probability inequality for $$m$$ m -END random variables and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 127-147, February.
    2. Aiting Shen & Andrei Volodin, 2017. "Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 605-625, November.
    3. Xuejun Wang & Xin Deng & Shuhe Hu, 2018. "On consistency of the weighted least squares estimators in a semiparametric regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 797-820, October.
    4. Xuejun Wang & Yi Wu & Rui Wang & Shuhe Hu, 2021. "On consistency of wavelet estimator in nonparametric regression models," Statistical Papers, Springer, vol. 62(2), pages 935-962, April.
    5. 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.
    6. Xuejun Wang & Yi Wu & Shuhe Hu & Nengxiang Ling, 2020. "Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models," Statistical Papers, Springer, vol. 61(3), pages 1147-1180, June.
    7. Yi Wu & Xuejun Wang & Aiting Shen, 2023. "Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.
    8. Jin Yu Zhou & Ji Gao Yan & Fei Du, 2023. "Complete and Complete f -Moment Convergence for Arrays of Rowwise END Random Variables and Some Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1307-1330, August.
    9. Mengmei Xi & Rui Wang & Zhaoyang Cheng & Xuejun Wang, 2020. "Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications," Statistical Papers, Springer, vol. 61(4), pages 1663-1684, August.
    10. Yi Wu & Xuejun Wang & Aiting Shen, 2021. "Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications," Statistical Papers, Springer, vol. 62(5), pages 2169-2194, October.
    11. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
    12. 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.
    13. Nan Cheng & Chao Lu & Jibing Qi & Xuejun Wang, 2022. "Complete moment convergence for randomly weighted sums of extended negatively dependent random variables with application to semiparametric regression models," Statistical Papers, Springer, vol. 63(2), pages 397-419, April.
    14. Yan, Ji Gao, 2018. "On Complete Convergence in Marcinkiewicz-Zygmund Type SLLN for END Random Variables and its Applications," IRTG 1792 Discussion Papers 2018-042, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    15. He, Wei & Cheng, Dongya & Wang, Yuebao, 2013. "Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 331-338.
    16. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    17. Thuan, Nguyen Tran & Quang, Nguyen Van, 2016. "Negative association and negative dependence for random upper semicontinuous functions, with applications," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 44-57.
    18. Gao Qingwu & Gu Peng & Jin Na, 2012. "Asymptotic Behavior of the Finite-Time Ruin Probability with Constant Interest Force and WUOD Heavy-Tailed Claims," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(1), pages 1-16, February.
    19. Kuczmaszewska, Anna & Yan, Ji Gao, 2018. "On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables," IRTG 1792 Discussion Papers 2018-041, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    20. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0966-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.