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The Bahadur representation for sample quantiles under weak dependence

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  • Sun, Shuxia

Abstract

In this paper, we give a Bahadur representation of sample quantiles based on strongly mixing random variables under polynomially decaying rate. Our results extend Theorems 1 and 2 of Yoshihara [1995. The Bahadur representation of sample quantile for sequences of strongly mixing random variables. Statist. Probab. Lett. 24, 299-304].

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  • Sun, Shuxia, 2006. "The Bahadur representation for sample quantiles under weak dependence," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1238-1244, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1238-1244
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    References listed on IDEAS

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    1. 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.
    2. Yoshihara, Ken-ichi, 1995. "The Bahadur representation of sample quantiles for sequences of strongly mixing random variables," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 299-304, September.
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    1. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    2. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    3. Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.
    4. Dudek, Dagmara & Kuczmaszewska, Anna, 2025. "The Bahadur representation for sample quantiles of ρ-mixing random variables," Statistics & Probability Letters, Elsevier, vol. 221(C).
    5. 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.
    6. Wendler, Martin, 2011. "Bahadur representation for U-quantiles of dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1064-1079, July.
    7. Santanu Dutta & Tushar Kanti Powdel, 2023. "Modeling Long Term Return Distribution and Nonparametric Market Risk Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 257-289, May.
    8. Sharipov, Olimjon Sh. & Wendler, Martin, 2013. "Normal limits, nonnormal limits, and the bootstrap for quantiles of dependent data," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1028-1035.

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