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Variance estimation in censored quantile regression via induced smoothing

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  • Pang, Lei
  • Lu, Wenbin
  • Wang, Huixia Judy
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    Abstract

    Statistical inference in censored quantile regression is challenging, partly due to the unsmoothness of the quantile score function. A new procedure is developed to estimate the variance of the Bang and Tsiatis inverse-censoring-probability weighted estimator for censored quantile regression by employing the idea of induced smoothing. The proposed variance estimator is shown to be asymptotically consistent. In addition, a numerical study suggests that the proposed procedure performs well in finite samples, and it is computationally more efficient than the commonly used bootstrap method.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 4 ()
    Pages: 785-796

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:785-796

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Censored quantile regression; Smoothing; Survival analysis; Variance estimation;

    References

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    1. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
    2. Peng, Limin & Huang, Yijian, 2008. "Survival Analysis With Quantile Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 637-649, June.
    3. Joel L. Horowitz, 1998. "Bootstrap Methods for Covariance Structures," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 39-61.
    4. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
    5. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    6. Yoon-Jae Whang, 2003. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Econometrics 0310005, EconWPA.
    7. Fu, Liya & Wang, You-Gan & Bai, Zhidong, 2010. "Rank regression for analysis of clustered data: A natural induced smoothing approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1036-1050, April.
    8. B. M. Brown & You-Gan Wang, 2005. "Standard errors and covariance matrices for smoothed rank estimators," Biometrika, Biometrika Trust, vol. 92(1), pages 149-158, March.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.
    11. Heller, Glenn, 2007. "Smoothed Rank Regression With Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 552-559, June.
    12. Lynn M. Johnson & Robert L. Strawderman, 2009. "Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data," Biometrika, Biometrika Trust, vol. 96(3), pages 577-590.
    13. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
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