IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i3d10.1007_s00362-025-01690-1.html
   My bibliography  Save this article

The uniformly complete consistency of generalized edge frequency polygon estimator for asymptotically negatively associated samples and an application

Author

Listed:
  • Meimei Ge

    (Anhui University
    Chuzhou University)

  • Yan Wang

    (Chizhou University)

  • Xin Deng

    (Chuzhou University)

  • Xuejun Wang

    (Anhui University)

  • Aiting Shen

    (Anhui University)

Abstract

This paper mainly studies the uniformly complete consistency and the convergence rate of generalized edge frequency polygon estimator for asymptotically negatively associated samples under some general conditions. As an application, the uniformly complete consistency and the corresponding rate of hazard rate function estimator are also obtained. In addition, simulations are also presented to verify the validity of the theoretical results based on finite samples.

Suggested Citation

  • Meimei Ge & Yan Wang & Xin Deng & Xuejun Wang & Aiting Shen, 2025. "The uniformly complete consistency of generalized edge frequency polygon estimator for asymptotically negatively associated samples and an application," Statistical Papers, Springer, vol. 66(3), pages 1-23, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01690-1
    DOI: 10.1007/s00362-025-01690-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-025-01690-1
    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/s00362-025-01690-1?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. Xuejun Wang & Yi Wu & Shuhe Hu, 2019. "The Berry–Esseen bounds of the weighted estimator in a nonparametric regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1143-1162, October.
    2. Lardjane, Salim, 2022. "Strong uniform consistency of the Frequency Polygon density estimator for stable non-anticipative stochastic processes," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. Tang, Xufei & Xi, Mengmei & Wu, Yi & Wang, Xuejun, 2018. "Asymptotic normality of a wavelet estimator for asymptotically negatively associated errors," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 191-201.
    4. Ahmad Younso, 2023. "Consistency of the frequency polygon estimators of density mode for strongly mixing processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(7), pages 2182-2197, April.
    5. Aiting Shen & Huiling Tao & Xuejun Wang, 2020. "The asymptotic properties for the estimators of the survival function and failure rate function based on WOD samples," Statistical Papers, Springer, vol. 61(6), pages 2671-2684, December.
    6. Mi-Hwa Ko, 2023. "Some limiting behavior of the maximum of the partial sum for asymptotically negatively associated random vectors in Hilbert space," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(11), pages 3598-3611, June.
    7. Xin Yang, 2017. "Uniform strong consistency of histogram density estimation for dependent process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1709-1719, February.
    8. Dong, Jianping & Zheng, Chuang, 2001. "Generalized edge frequency polygon for density estimation," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 137-145, November.
    9. Carbon, Michel & Garel, Bernard & Tran, Lanh Tat, 1997. "Frequency polygons for weakly dependent processes," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 1-13, April.
    10. Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
    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. Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2016. "Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 296-321, June.
    2. Ahmad Younso, 2023. "On the consistency of mode estimate for spatially dependent data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 343-372, April.
    3. Gao, Jiti & Anh, Vo, 2000. "A central limit theorem for a random quadratic form of strictly stationary processes," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 69-79, August.
    4. Dagmara Dudek & Anna Kuczmaszewska, 2024. "Some practical and theoretical issues related to the quantile estimators," Statistical Papers, Springer, vol. 65(6), pages 3917-3933, August.
    5. Llop, P. & Forzani, L. & Fraiman, R., 2011. "On local times, density estimation and supervised classification from functional data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 73-86, January.
    6. Labrador, Boris, 2008. "Strong pointwise consistency of the kT -occupation time density estimator," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1128-1137, July.
    7. Francesco Bravo & Ba M. Chu & David T. Jacho-Chávez, 2017. "Semiparametric estimation of moment condition models with weakly dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 108-136, January.
    8. Aiting Shen & Huiling Tao & Xuejun Wang, 2020. "The asymptotic properties for the estimators of the survival function and failure rate function based on WOD samples," Statistical Papers, Springer, vol. 61(6), pages 2671-2684, December.
    9. Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    10. Mohamed El Machkouri, 2013. "On the asymptotic normality of frequency polygons for strongly mixing spatial processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 193-206, October.
    11. Lardjane, Salim, 2022. "Strong uniform consistency of the Frequency Polygon density estimator for stable non-anticipative stochastic processes," Statistics & Probability Letters, Elsevier, vol. 189(C).
    12. Michel Carbon & Thierry Duchesne, 2024. "Multivariate frequency polygon for stationary random fields," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(2), pages 263-287, April.
    13. Boris Labrador, 2009. "Rates of strong uniform convergence of the k T -occupation time density estimator," Statistical Inference for Stochastic Processes, Springer, vol. 12(3), pages 269-283, October.
    14. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    15. Gao, Jiti & Tong, Howell, 2002. "Nonparametric and semiparametric regression model selection," MPRA Paper 11987, University Library of Munich, Germany, revised Feb 2004.
    16. Chu, Ba & Huynh, Kim & Jacho-Chavez, David, 2013. "Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours," MPRA Paper 79670, University Library of Munich, Germany, revised 2012.
    17. Yi Wu & Xuejun Wang, 2025. "On Berry–Esséen bound of frequency polygon estimation under $$\rho $$ ρ -mixing samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(1), pages 19-41, January.
    18. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    19. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2022. "Universal Local Linear Kernel Estimators in Nonparametric Regression," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    20. Livasoa Andriamampionona & Victor Harison & Michel Harel, 2024. "Non-Parametric Estimation of the Renewal Function for Multidimensional Random Fields," Mathematics, MDPI, vol. 12(12), pages 1-22, June.

    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:66:y:2025:i:3:d:10.1007_s00362-025-01690-1. 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.