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Asymptotics for censored regression quantiles

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  • Stephen Portnoy
  • Guixian Lin

Abstract

It has been difficult to generalise Kaplan–Meier approaches to censored regression data under the minimal condition that censoring and response are conditionally independent given the explanatory variables. Portnoy [S. Portnoy, Censored regression quantiles, J. Am. Stat. Assoc. 98 (2003), pp. 1001–1012.] provided such a generalisation based on the paradigm of censored quantile regression. However, previous research has only provided consistency results for this approach. The results here provide an asymptotic distribution theory under relatively mild conditions for a gridded version of the algorithm in Portnoy [S. Portnoy, Censored regression quantiles, J. Am. Stat. Assoc. 98 (2003), pp. 1001–1012.], and show that the asymptotics for censored regression quantiles are an exact generalisation of those for the Kaplan–Meier estimator in one sample.

Suggested Citation

  • Stephen Portnoy & Guixian Lin, 2010. "Asymptotics for censored regression quantiles," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 115-130.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:115-130
    DOI: 10.1080/10485250903105009
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    References listed on IDEAS

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    1. Neocleous, Tereza & Portnoy, Stephen, 2008. "On monotonicity of regression quantile functions," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1226-1229, August.
    2. Portnoy S., 2003. "Censored Regression Quantiles," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1001-1012, January.
    3. Neocleous, Tereza & Branden, Karlien Vanden & Portnoy, Stephen, 2006. "Correction to Censored Regression Quantiles by S. Portnoy, 98 (2003), 10011012," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 860-861, June.
    4. 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.
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    Cited by:

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    2. Jin-Jian Hsieh & Cheng-Chih Hsieh, 2023. "Quantile Regression Based on the Weighted Approach with Dependent Truncated Data," Mathematics, MDPI, vol. 11(17), pages 1-13, August.
    3. Shuang Ji & Limin Peng & Yu Cheng & HuiChuan Lai, 2012. "Quantile Regression for Doubly Censored Data," Biometrics, The International Biometric Society, vol. 68(1), pages 101-112, March.
    4. Peng, Limin, 2012. "Self-consistent estimation of censored quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 368-379.
    5. Kyu Hyun Kim & Daniel J. Caplan & Sangwook Kang, 2023. "Smoothed quantile regression for censored residual life," Computational Statistics, Springer, vol. 38(2), pages 1001-1022, June.
    6. Yuanshan Wu & Guosheng Yin, 2013. "Cure Rate Quantile Regression for Censored Data With a Survival Fraction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1517-1531, December.
    7. Jin-Jian Hsieh & Hong-Rui Wang, 2018. "Quantile regression based on counting process approach under semi-competing risks data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 395-419, April.
    8. Xiaoyan Sun & Limin Peng & Yijian Huang & HuiChuan J. Lai, 2016. "Generalizing Quantile Regression for Counting Processes With Applications to Recurrent Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 145-156, March.
    9. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.
    10. Seokwoo Jake Choi & Stephen Portnoy, 2016. "Quantile Autoregression for Censored Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(5), pages 603-623, September.
    11. Portnoy, Stephen, 2014. "The jackknife’s edge: Inference for censored regression quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 273-281.

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