IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i4d10.1007_s00362-016-0847-7.html
   My bibliography  Save this article

Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity

Author

Listed:
  • Y. Andriyana

    (KU Leuven
    Universitas Padjadjaran)

  • I. Gijbels

    (KU Leuven)

  • A. Verhasselt

    (Universiteit Hasselt)

Abstract

Quantile regression is an important tool for describing the characteristics of conditional distributions. Population conditional quantile functions cannot cross for different quantile orders. Unfortunately estimated regression quantile curves often violate this and cross each other, which can be very annoying for interpretations and further analysis. In this paper we are concerned with flexible varying-coefficient modelling, and develop methods for quantile regression that ensure that the estimated quantile curves do not cross. A second aim of the paper is to allow for some heteroscedasticity in the error modelling, and to also estimate the associated variability function. We investigate the finite-sample performances of the discussed methods via simulation studies. Some applications to real data illustrate the use of the methods in practical settings.

Suggested Citation

  • Y. Andriyana & I. Gijbels & A. Verhasselt, 2018. "Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity," Statistical Papers, Springer, vol. 59(4), pages 1589-1621, December.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-016-0847-7
    DOI: 10.1007/s00362-016-0847-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0847-7
    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/s00362-016-0847-7?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. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    2. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280, April.
    3. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    4. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    5. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    6. Anestis Antoniadis & Irène Gijbels & Mila Nikolova, 2011. "Penalized likelihood regression for generalized linear models with non-quadratic penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 585-615, June.
    7. Zhao, Zhibiao & Xiao, Zhijie, 2014. "Efficient Regressions Via Optimally Combining Quantile Information," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1272-1314, December.
    8. Hu Yang & Huilan Liu, 2016. "Penalized weighted composite quantile estimators with missing covariates," Statistical Papers, Springer, vol. 57(1), pages 69-88, March.
    9. Holger Dette & Stanislav Volgushev, 2008. "Non‐crossing non‐parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627, July.
    10. Y. Andriyana & I. Gijbels & A. Verhasselt, 2014. "P-splines quantile regression estimation in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 153-194, March.
    11. Yufeng Liu & Yichao Wu, 2011. "Simultaneous multiple non-crossing quantile regression estimation using kernel constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 415-437.
    12. Lamarche, Carlos, 2010. "Robust penalized quantile regression estimation for panel data," Journal of Econometrics, Elsevier, vol. 157(2), pages 396-408, August.
    13. Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
    14. Eilers, Paul H.C. & Currie, Iain D. & Durban, Maria, 2006. "Fast and compact smoothing on large multidimensional grids," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 61-76, January.
    15. Neumeyer, Natalie, 2009. "Testing independence in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1551-1566, August.
    16. Koenker, Roger, 1984. "A note on L-estimates for linear models," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 323-325, December.
    17. Karlsson, Maria & Lindmark, Anita, 2014. "truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i14).
    18. Jiancheng Jiang & Xuejun Jiang & Xinyuan Song, 2014. "Weighted composite quantile regression estimation of DTARCH models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 1-23, February.
    19. T. J. Cole, 1988. "Fitting Smoothed Centile Curves to Reference Data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 151(3), pages 385-406, May.
    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. Kim, Joonpyo & Oh, Hee-Seok, 2020. "Pseudo-quantile functional data clustering," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    2. Bertho Tantular & Budi Nurani Ruchjana & Yudhie Andriyana & Anneleen Verhasselt, 2023. "Quantile Regression in Space-Time Varying Coefficient Model of Upper Respiratory Tract Infections Data," Mathematics, MDPI, vol. 11(4), pages 1-16, February.

    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. Tomohiro Ando & Jushan Bai, 2020. "Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 266-279, January.
    2. Y. Andriyana & I. Gijbels & A. Verhasselt, 2014. "P-splines quantile regression estimation in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 153-194, March.
    3. Sabine Schnabel & Paul Eilers, 2013. "Simultaneous estimation of quantile curves using quantile sheets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 77-87, January.
    4. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    5. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    6. Songhao Wang & Szu Hui Ng & William Benjamin Haskell, 2022. "A Multilevel Simulation Optimization Approach for Quantile Functions," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 569-585, January.
    7. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    8. Ilaria Lucrezia Amerise, 2013. "Weighted Non-Crossing Quantile Regressions," Working Papers 201308, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    9. Liwen Zhang & Huixia Judy Wang & Zhongyi Zhu, 2017. "Composite change point estimation for bent line quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 145-168, February.
    10. Paolo Frumento & Nicola Salvati, 2021. "Parametric modeling of quantile regression coefficient functions with count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1237-1258, October.
    11. Yuzhi Cai, 2016. "A Comparative Study Of Monotone Quantile Regression Methods For Financial Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-16, May.
    12. Y. Andriyana & I. Gijbels, 2017. "Quantile regression in heteroscedastic varying coefficient models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 151-176, April.
    13. Amadou Barry & Karim Oualkacha & Arthur Charpentier, 2023. "Alternative fixed-effects panel model using weighted asymmetric least squares regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 819-841, September.
    14. Tang, Yanlin & Wang, Huixia Judy, 2015. "Penalized regression across multiple quantiles under random censoring," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 132-146.
    15. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    16. D Barrera & S Crépey & E Gobet & Hoang-Dung Nguyen & B Saadeddine, 2022. "Learning Value-at-Risk and Expected Shortfall," Working Papers hal-03775901, HAL.
    17. Xenxo Vidal-Llana & Carlos Salort Sánchez & Vincenzo Coia & Montserrat Guillen, 2022. ""Non-Crossing Dual Neural Network: Joint Value at Risk and Conditional Tail Expectation estimations with non-crossing conditions"," IREA Working Papers 202215, University of Barcelona, Research Institute of Applied Economics, revised Oct 2022.
    18. Mohamed Ouhourane & Yi Yang & Andréa L. Benedet & Karim Oualkacha, 2022. "Group penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 495-529, September.
    19. Amadou Barry & Karim Oualkacha & Arthur Charpentier, 2021. "Weighted asymmetric least squares regression with fixed-effects," Papers 2108.04737, arXiv.org.
    20. D Barrera & S Cr'epey & E Gobet & Hoang-Dung Nguyen & B Saadeddine, 2022. "Learning Value-at-Risk and Expected Shortfall," Papers 2209.06476, arXiv.org.

    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:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-016-0847-7. 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.