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The Bahadur representation for sample quantiles under weak dependence

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  • Sun, Shuxia
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    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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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4HYMSJS-2/2/3c5c6f81045f79696ea4664315e1517b
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 76 (2006)
    Issue (Month): 12 (July)
    Pages: 1238-1244

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    Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1238-1244

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    Keywords: Bahadur representation Sample quantile Strongly mixing;

    References

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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, Elsevier, vol. 24(4), pages 299-304, September.
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    Cited by:
    1. Sharipov, Olimjon Sh. & Wendler, Martin, 2013. "Normal limits, nonnormal limits, and the bootstrap for quantiles of dependent data," Statistics & Probability Letters, Elsevier, Elsevier, vol. 83(4), pages 1028-1035.
    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. Qinchi Zhang & Wenzhi Yang & Shuhe Hu, 2014. "On Bahadur representation for sample quantiles under α-mixing sequence," Statistical Papers, Springer, Springer, vol. 55(2), pages 285-299, May.

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