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Variable selection and coefficient estimation via composite quantile regression with randomly censored data

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  • Jiang, Rong
  • Qian, Weimin
  • Zhou, Zhangong
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    Abstract

    Composite quantile regression with randomly censored data is studied. Moreover, adaptive LASSO methods for composite quantile regression with randomly censored data are proposed. The consistency, asymptotic normality and oracle property of the proposed estimators are established. The proposals are illustrated via simulation studies and the Australian AIDS dataset.

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    Bibliographic Info

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

    Volume (Year): 82 (2012)
    Issue (Month): 2 ()
    Pages: 308-317

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:308-317

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    Related research

    Keywords: Kaplan–Meier estimator; Randomly censored data; Composite quantile regression; Variable selection; LASSO;

    References

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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, 9.
    3. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, Elsevier, vol. 25(3), pages 303-325, July.
    4. Peng, Limin & Huang, Yijian, 2008. "Survival Analysis With Quantile Regression Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 103, pages 637-649, June.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 653-672, May.
    7. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    8. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69.
    9. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
    10. Koenker R. & Geling O., 2001. "Reappraising Medfly Longevity: A Quantile Regression Survival Analysis," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 458-468, June.
    11. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 25, pages 347-355, July.
    12. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    13. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, Elsevier, vol. 32(1), pages 143-155, June.
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    Cited by:
    1. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 64(C), pages 180-191.
    2. Wang, Jiang-Feng & Ma, Wei-Min & Zhang, Hui-Zeng & Wen, Li-Min, 2013. "Asymptotic normality for a local composite quantile regression estimator of regression function with truncated data," Statistics & Probability Letters, Elsevier, Elsevier, vol. 83(6), pages 1571-1579.

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