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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
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    References listed on IDEAS

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    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. 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.
    5. Dong, Jianping & Zheng, Chuang, 2001. "Generalized edge frequency polygon for density estimation," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 137-145, November.
    6. 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.
    7. 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.
    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. 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.
    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.
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