IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v48y2021i2p655-688.html
   My bibliography  Save this article

A new lack‐of‐fit test for quantile regression with censored data

Author

Listed:
  • Mercedes Conde‐Amboage
  • Ingrid Van Keilegom
  • Wenceslao González‐Manteiga

Abstract

A new lack‐of‐fit test for quantile regression models will be presented for the case where the response variable is right‐censored. The test is based on the cumulative sum of residuals, and it extends the ideas of He and Zhu (2003) to censored quantile regression. It will be shown that the empirical process associated with the test statistic converges to a Gaussian process under the null hypothesis and is consistent. To approximate the critical values of the test, a bootstrap mechanism will be used. A simulation study will be carried out to study the performance of the new test in comparison with other tests available in the literature. Finally, a real data application will be presented to show the good properties of the new lack‐of‐fit test in practice.

Suggested Citation

  • Mercedes Conde‐Amboage & Ingrid Van Keilegom & Wenceslao González‐Manteiga, 2021. "A new lack‐of‐fit test for quantile regression with censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 655-688, June.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:2:p:655-688
    DOI: 10.1111/sjos.12512
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12512
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12512?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
    ---><---

    References listed on IDEAS

    as
    1. De Backer, Mickaël & El Ghouch, Anouar & Van Keilegom, Ingrid, 2020. "Linear censored quantile regression: A novel minimum‐distance approach," LIDAM Reprints ISBA 2020010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
    3. 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.
    4. Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2006. "Comparison of Regression Curves with Censored Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 409-434, September.
    5. De Backer, Mickael & El Ghouch, Anouar & Van Keilegom, Ingrid, 2017. "Semiparametric copula quantile regression for complete or censored data," LIDAM Reprints ISBA 2017020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Yang, Seong Jun & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Varying coefficient models having different smoothing variables with randomly censored data," LIDAM Reprints ISBA 2014008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. De Backer, Mickael & El Ghouch, Anouar & Van Keilegom, Ingrid, 2019. "An Adapted Loss Function for Censored Quantile Regression," LIDAM Reprints ISBA 2019054, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Ingrid Van Keilegom & Noël Veraverbeke, 1997. "Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 467-491, September.
    9. Yingwei Peng & Jeremy M. G. Taylor, 2017. "Residual-based model diagnosis methods for mixture cure models," Biometrics, The International Biometric Society, vol. 73(2), pages 495-505, June.
    10. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    11. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    12. Yuanshan Wu & Guosheng Yin, 2015. "Conditional quantile screening in ultrahigh-dimensional heterogeneous data," Biometrika, Biometrika Trust, vol. 102(1), pages 65-76.
    13. Colling, Benjamin & Van Keilegom, Ingrid, 2017. "Goodness-of-fit tests in semiparametric transformation models using the integrated regression function," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 10-30.
    14. Mickaël De Backer & Anouar El Ghouch & Ingrid Van Keilegom, 2019. "An Adapted Loss Function for Censored Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1126-1137, July.
    15. Colling, Benjamin & Van Keilegom, Ingrid, 2017. "Goodness-of-fit tests in semiparametric transformation models using the integrated regression function," LIDAM Reprints ISBA 2017024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Ingrid Keilegom & Wenceslao González Manteiga & César Sánchez Sellero, 2008. "Goodness-of-fit tests in parametric regression based on the estimation of the error distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 401-415, August.
    17. Zheng, John Xu, 1998. "A Consistent Nonparametric Test Of Parametric Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 123-138, February.
    18. Huixia Judy Wang & Ian W. McKeague & Min Qian, 2018. "Testing for marginal linear effects in quantile regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 433-452, March.
    19. Anna, Petrenko, 2016. "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(1), March.
    20. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    21. Gang Li & Somnath Datta, 2001. "A Bootstrap Approach to Nonparametric Regression for Right Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 708-729, December.
    22. 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.
    23. 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.
    24. Hendrik P. Lopuhaä & Eni Musta, 2018. "Smoothed Isotonic Estimators of a Monotone Baseline Hazard in the Cox Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 753-791, September.
    25. Candida Geerdens & Paul Janssen & Ingrid Van Keilegom, 2020. "Goodness-of-fit test for a parametric survival function with cure fraction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 768-792, September.
    26. Lopez, O. & Patilea, V., 2009. "Nonparametric lack-of-fit tests for parametric mean-regression models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 210-230, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Natalie Neumeyer & Miguel A. Delgado & Lajos Horváth & Simos Meintanis & Emanuele Taufer & Lixing Zhu, 2021. "4th Workshop on Goodness‐of‐Fit, Change‐Point, and Related Problems, Trento, 2019," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 371-374, June.

    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. Jad Beyhum & Lorenzo Tedesco & Ingrid Van Keilegom, 2022. "Instrumental variable quantile regression under random right censoring," Papers 2209.01429, arXiv.org, revised Feb 2023.
    2. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    3. Gabriela M. Rodrigues & Edwin M. M. Ortega & Gauss M. Cordeiro & Roberto Vila, 2023. "Quantile Regression with a New Exponentiated Odd Log-Logistic Weibull Distribution," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    4. 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.
    5. Worku Biyadgie Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2024. "Two-piece distribution based semi-parametric quantile regression for right censored data," Statistical Papers, Springer, vol. 65(5), pages 2775-2810, July.
    6. Yue Zhao & Ingrid Van Keilegom & Shanshan Ding, 2022. "Envelopes for censored quantile regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1562-1585, December.
    7. Kloodt, Nick & Neumeyer, Natalie, 2020. "Specification tests in semiparametric transformation models — A multiplier bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    8. Fan, Yanqin & Liu, Ruixuan, 2018. "Partial identification and inference in censored quantile regression," Journal of Econometrics, Elsevier, vol. 206(1), pages 1-38.
    9. García, A., 2016. "Oaxaca-Blinder Type Counterfactual Decomposition Methods for Duration Outcomes," Documentos de Trabajo 14186, Universidad del Rosario.
    10. Francesco Bravo, 2020. "Semiparametric quantile regression with random censoring," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 265-295, February.
    11. 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).
    12. Ying Cui & Limin Peng, 2022. "Assessing dynamic covariate effects with survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 675-699, October.
    13. 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.
    14. Jacobo Uña-Álvarez & Noël Veraverbeke, 2013. "Generalized copula-graphic estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 343-360, June.
    15. Miguel A Delgado & Andrés García-Suaza & Pedro H C Sant’Anna, 2022. "Distribution regression in duration analysis: an application to unemployment spells [Lecture notes in statistics: Proceedings]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 675-698.
    16. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    17. Lorenzo Tedesco & Jad Beyhum & Ingrid Van Keilegom, 2023. "Instrumental variable estimation of the proportional hazards model by presmoothing," Papers 2309.02183, arXiv.org.
    18. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 614-632, August.
    19. Olivier Lopez & Xavier Milhaud & Pierre-Emmanuel Thérond, 2016. "Tree-based censored regression with applications in insurance," Post-Print hal-01141228, HAL.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:48:y:2021:i:2:p:655-688. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.