IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v127y2018icp172-186.html
   My bibliography  Save this article

Bayesian non-parametric simultaneous quantile regression for complete and grid data

Author

Listed:
  • Das, Priyam
  • Ghosal, Subhashis

Abstract

Bayesian methods for non-parametric quantile regression have been considered with multiple continuous predictors ranging values in the unit interval. Two methods are proposed based on assuming that either the quantile function or the distribution function is smooth in the explanatory variables and is expanded in tensor product of B-spline basis functions. Unlike other existing methods of non-parametric quantile regressions, the proposed methods estimate the whole quantile function instead of estimating on a grid of quantiles. Priors on the coefficients of the B-spline expansion are put in such a way that the monotonicity of the estimated quantile levels are maintained unlike local polynomial quantile regression methods. The proposed methods are also modified for quantile grid data where only the percentile range of each response observations are known. A comparative simulation study of the performances of the proposed methods and some other existing methods are provided in terms of prediction mean squared errors and mean L1-errors over the quartiles. The proposed methods are used to estimate the quantiles of US household income data and North Atlantic hurricane intensity data.

Suggested Citation

  • Das, Priyam & Ghosal, Subhashis, 2018. "Bayesian non-parametric simultaneous quantile regression for complete and grid data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 172-186.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:172-186
    DOI: 10.1016/j.csda.2018.04.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318300963
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.04.007?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. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November.
    2. Jooyong Shim & Changha Hwang & Kyung Seok, 2009. "Non-crossing quantile regression via doubly penalized kernel machine," Computational Statistics, Springer, vol. 24(1), pages 83-94, February.
    3. James B. Elsner & James P. Kossin & Thomas H. Jagger, 2008. "The increasing intensity of the strongest tropical cyclones," Nature, Nature, vol. 455(7209), pages 92-95, September.
    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. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    6. Das, Priyam & Ghosal, Subhashis, 2017. "Bayesian quantile regression using random B-spline series prior," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 121-143.
    7. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    8. Brian J. Reich & Luke B. Smith, 2013. "Bayesian Quantile Regression for Censored Data," Biometrics, The International Biometric Society, vol. 69(3), pages 651-660, September.
    9. Reich, Brian J. & Fuentes, Montserrat & Dunson, David B., 2011. "Bayesian Spatial Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 6-20.
    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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. Brian J. Reich, 2012. "Spatiotemporal quantile regression for detecting distributional changes in environmental processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(4), pages 535-553, August.
    13. Athanasios Kottas & Milovan Krnjajić, 2009. "Bayesian Semiparametric Modelling in Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 297-319, June.
    14. Yun Yang & Surya T. Tokdar, 2017. "Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1107-1120, July.
    15. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    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. Priyam Das, 2021. "Recursive Modified Pattern Search on High-Dimensional Simplex : A Blackbox Optimization Technique," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 440-483, November.
    2. Yunyun Wang & Tatsushi Oka & Dan Zhu, 2024. "Inflation Target at Risk: A Time-varying Parameter Distributional Regression," Papers 2403.12456, arXiv.org.
    3. Gijbels, Irène & Karim, Rezaul & Verhasselt, Anneleen, 2021. "Semiparametric quantile regression using family of quantile-based asymmetric densities," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    4. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    5. Xianhua Wu & Jiqiang Zhao & Yun Kuai & Ji Guo & Ge Gao, 2021. "Construction and verification of a rainstorm death risk index based on grid data fusion: a case study of the Beijing rainstorm on July 21, 2012," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(3), pages 2293-2318, July.
    6. Bhattacharya, Indrabati & Ghosal, Subhashis, 2021. "Bayesian multivariate quantile regression using Dependent Dirichlet Process prior," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    7. 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.

    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. Das, Priyam & Ghosal, Subhashis, 2017. "Bayesian quantile regression using random B-spline series prior," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 121-143.
    2. Rodrigues, T. & Dortet-Bernadet, J.-L. & Fan, Y., 2019. "Simultaneous fitting of Bayesian penalised quantile splines," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 93-109.
    3. 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.
    4. Yun Yang & Surya T. Tokdar, 2017. "Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1107-1120, July.
    5. Fabrizi, Enrico & Salvati, Nicola & Trivisano, Carlo, 2020. "Robust Bayesian small area estimation based on quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    6. Luke B. Smith & Brian J. Reich & Amy H. Herring & Peter H. Langlois & Montserrat Fuentes, 2015. "Multilevel quantile function modeling with application to birth outcomes," Biometrics, The International Biometric Society, vol. 71(2), pages 508-519, June.
    7. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
    8. Viviana Carcaiso & Leonardo Grilli, 2023. "Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1061-1082, October.
    9. Yingying Hu & Huixia Judy Wang & Xuming He & Jianhua Guo, 2021. "Bayesian joint-quantile regression," Computational Statistics, Springer, vol. 36(3), pages 2033-2053, September.
    10. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
    11. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    12. Bhattacharya, Indrabati & Ghosal, Subhashis, 2021. "Bayesian multivariate quantile regression using Dependent Dirichlet Process prior," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    13. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    14. Priyam Das & Christine B. Peterson & Yang Ni & Alexandre Reuben & Jiexin Zhang & Jianjun Zhang & Kim‐Anh Do & Veerabhadran Baladandayuthapani, 2023. "Bayesian hierarchical quantile regression with application to characterizing the immune architecture of lung cancer," Biometrics, The International Biometric Society, vol. 79(3), pages 2474-2488, September.
    15. Luke B. Smith, 2016. "Discussion," International Statistical Review, International Statistical Institute, vol. 84(3), pages 359-362, December.
    16. A Ford Ramsey, 2020. "Probability Distributions of Crop Yields: A Bayesian Spatial Quantile Regression Approach," American Journal of Agricultural Economics, John Wiley & Sons, vol. 102(1), pages 220-239, January.
    17. Henry R. Scharf & Xinyi Lu & Perry J. Williams & Mevin B. Hooten, 2022. "Constructing Flexible, Identifiable and Interpretable Statistical Models for Binary Data," International Statistical Review, International Statistical Institute, vol. 90(2), pages 328-345, August.
    18. Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
    19. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    20. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.

    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:eee:csdana:v:127:y:2018:i:c:p:172-186. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.