IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v28y2019i4d10.1007_s10260-019-00450-4.html
   My bibliography  Save this article

Single index quantile regression for censored data

Author

Listed:
  • Eliana Christou

    (University of North Carolina at Charlotte)

  • Michael G. Akritas

    (The Pennsylvania State University)

Abstract

Quantile regression (QR) has become a popular method of data analysis, especially when the error term is heteroscedastic. It is particularly relevant for the analysis of censored survival data as an alternative to proportional hazards and the accelerated failure time models. Such data occur frequently in biostatistics, environmental sciences, social sciences and econometrics. There is a large body of work for linear/nonlinear QR models for censored data, but it is only recently that the single index quantile regression (SIQR) model has received some attention. However, the only existing method for fitting the SIQR model for censored data uses an iterative algorithm and no asymptotic theory for the resulting estimator of the parametric component is given. We propose a non-iterative estimation algorithm and derive the asymptotic distribution of the proposed estimator under heteroscedasticity. Results from simulation studies evaluating the finite sample performance of the proposed estimator are reported.

Suggested Citation

  • Eliana Christou & Michael G. Akritas, 2019. "Single index quantile regression for censored data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 655-678, December.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:4:d:10.1007_s10260-019-00450-4
    DOI: 10.1007/s10260-019-00450-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-019-00450-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-019-00450-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Eliana Christou & Michael G. Akritas, 2018. "Variable selection in heteroscedastic single-index quantile regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(24), pages 6019-6033, December.
    3. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
    4. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2013. "Global Bahadur Representation For Nonparametric Censored Regression Quantiles And Its Applications," Econometric Theory, Cambridge University Press, vol. 29(5), pages 941-968, October.
    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. Maura Mezzetti & Paolo Giudici, 1999. "Monte Carlo methods for nonparametric survival model determination," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 8(1), pages 49-60, April.
    7. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    8. Koenker R. & Geling O., 2001. "Reappraising Medfly Longevity: A Quantile Regression Survival Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 458-468, June.
    9. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    11. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    12. A. Gannoun & Jérôme Saracco & K. Yu, 2007. "Comparison of kernel estimators of conditional distribution function and quantile regression under censoring for survival analysis," Post-Print hal-00153550, HAL.
    13. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    14. Christou, Eliana & Akritas, Michael G., 2016. "Single index quantile regression for heteroscedastic data," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 169-182.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2019. "Weighted quantile regression for censored data with application to export duration data," Statistical Papers, Springer, vol. 60(4), pages 1161-1192, August.
    2. Fan, Yanqin & Liu, Ruixuan, 2018. "Partial identification and inference in censored quantile regression," Journal of Econometrics, Elsevier, vol. 206(1), pages 1-38.
    3. De Backer, Mickael & El Ghouch, Anouar & Van Keilegom, Ingrid, 2017. "An Adapted Loss Function for Censored Quantile Regression," LIDAM Discussion Papers ISBA 2017003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Jiang, Rong & Qian, Weimin & Zhou, Zhangong, 2012. "Variable selection and coefficient estimation via composite quantile regression with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 308-317.
    5. Mickaël De Backer & Anouar El Ghouch & Ingrid Van Keilegom, 2020. "Linear censored quantile regression: A novel minimum‐distance approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1275-1306, December.
    6. 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.
    7. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2013. "Global Bahadur Representation For Nonparametric Censored Regression Quantiles And Its Applications," Econometric Theory, Cambridge University Press, vol. 29(5), pages 941-968, October.
    8. Lin, Guixian & He, Xuming & Portnoy, Stephen, 2012. "Quantile regression with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 797-812.
    9. Peng, Limin, 2012. "Self-consistent estimation of censored quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 368-379.
    10. Sungwon Lee & Joon H. Ro, 2020. "Nonparametric Tests for Conditional Quantile Independence with Duration Outcomes," Working Papers 2013, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    11. Elke Lüdemann & Ralf Wilke & Xuan Zhang, 2006. "Censored quantile regressions and the length of unemployment periods in West Germany," Empirical Economics, Springer, vol. 31(4), pages 1003-1024, November.
    12. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    13. Marcelo Cajias & Philipp Freudenreich & Anna Freudenreich, 2020. "Exploring the determinants of real estate liquidity from an alternative perspective: censored quantile regression in real estate research," Journal of Business Economics, Springer, vol. 90(7), pages 1057-1086, August.
    14. Chen, Songnian, 2019. "Quantile regression for duration models with time-varying regressors," Journal of Econometrics, Elsevier, vol. 209(1), pages 1-17.
    15. 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.
    16. Genya Kobayashi & Hideo Kozumi, 2012. "Bayesian analysis of quantile regression for censored dynamic panel data," Computational Statistics, Springer, vol. 27(2), pages 359-380, June.
    17. Akram Yazdani & Hojjat Zeraati & Mehdi Yaseri & Shahpar Haghighat & Ahmad Kaviani, 2022. "Laplace regression with clustered censored data," Computational Statistics, Springer, vol. 37(3), pages 1041-1068, July.
    18. Chen, Songnian, 2023. "Two-step estimation of censored quantile regression for duration models with time-varying regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 1310-1336.
    19. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    20. Xianghua Luo & Chiung-Yu Huang & Lan Wang, 2013. "Quantile Regression for Recurrent Gap Time Data," Biometrics, The International Biometric Society, vol. 69(2), pages 375-385, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:28:y:2019:i:4:d:10.1007_s10260-019-00450-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.