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Some practical and theoretical issues related to the quantile estimators

Author

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  • Dagmara Dudek

    (Lublin University of Technology)

  • Anna Kuczmaszewska

    (Lublin University of Technology)

Abstract

The paper contains the comparative analysis of the efficiency of different qunatile estimators for various distributions. Additionally, we show strong consistency of different quantile estimators and we study the Bahadur representation for each of the quantile estimators, when the sample is taken from NA, $$\varphi $$ φ , $$\rho ^*$$ ρ ∗ , $$\rho $$ ρ -mixing population.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:6:d:10.1007_s00362-024-01543-3
    DOI: 10.1007/s00362-024-01543-3
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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. Xiaoqin Li & Wenzhi Yang & Shuhe Hu & Xuejun Wang, 2011. "The Bahadur representation for sample quantile under NOD sequence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 59-65.
    3. Babu, Gutti Jogesh & Singh, Kesar, 1978. "On deviations between empirical and quantile processes for mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 532-549, December.
    4. Qinchi Zhang & Wenzhi Yang & Shuhe Hu, 2014. "On Bahadur representation for sample quantiles under α-mixing sequence," Statistical Papers, Springer, vol. 55(2), pages 285-299, May.
    5. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    6. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    7. Shao, Qi-Man & Su, Chun, 1999. "The law of the iterated logarithm for negatively associated random variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 139-148, September.
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    Cited by:

    1. Vladica S. Stojanović & Tanja Jovanović Spasojević & Mihailo Jovanović, 2024. "Laplace-Logistic Unit Distribution with Application in Dynamic and Regression Analysis," Mathematics, MDPI, vol. 12(14), pages 1-21, July.

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