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The Bahadur representation for kernel-type estimator of the quantile function under strong mixing and censored data

  • Ajami, M.
  • Fakoor, V.
  • Jomhoori, S.
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    In this paper, we consider the kernel-type estimator of the quantile function based on the kernel smoother under a censored dependent model. The Bahadur-type representation of the kernel smooth estimator is established, and from the Bahadur representation we can show that this estimator is strongly consistent.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211001246
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 8 (August)
    Pages: 1306-1310

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1306-1310
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    1. Sen, Pranab Kumar, 1972. "On the Bahadur representation of sample quantiles for sequences of [phi]-mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 77-95, March.
    2. Szeman Tse, 2005. "Quantile process for left truncated and right censored data," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(1), pages 61-69, March.
    3. 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.
    4. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(02), pages 258-289, February.
    5. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November.
    6. Fotopoulos, S. B. & Ahn, S. K., 1994. "Strong Approximation of the Quantile Processes and Its Applications under Strong Mixing Properties," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 17-45, October.
    7. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(02), pages 214-252, April.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    9. Xiang, X. J., 1995. "Bahadur Representation of the Kernel Quantile Estimator under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 193-209, August.
    10. Yu, Hao, 1996. "A note on strong approximation for quantile processes of strong mixing sequences," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 1-7, September.
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