IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v44y2017i5p798-810.html
   My bibliography  Save this article

Flexible objective Bayesian linear regression with applications in survival analysis

Author

Listed:
  • Francisco J. Rubio
  • Keming Yu

Abstract

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual assumption of normality of the errors in terms of heavy tails, asymmetry, and certain types of heteroscedasticity. We propose a general non-informative, scale-invariant, prior structure and provide sufficient conditions for the propriety of the posterior distribution of the model parameters, which cover cases when the response variables are censored. These results allow us to apply the proposed models in the context of survival analysis. This paper represents an extension to the Bayesian framework of the models proposed in [16]. We present a simulation study that shows good frequentist properties of the posterior credible intervals as well as point estimators associated to the proposed priors. We illustrate the performance of these models with real data in the context of survival analysis of cancer patients.

Suggested Citation

  • Francisco J. Rubio & Keming Yu, 2017. "Flexible objective Bayesian linear regression with applications in survival analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 798-810, April.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:5:p:798-810
    DOI: 10.1080/02664763.2016.1182138
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2016.1182138
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2016.1182138?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. Catalina A. Vallejos & Mark F. J. Steel, 2015. "Objective Bayesian Survival Analysis Using Shape Mixtures of Log-Normal Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 697-710, June.
    2. Nuttanan Wichitaksorn & Joanna J. J. Wang & S. T. Boris Choy & Richard Gerlach, 2015. "Analyzing return asymmetry and quantiles through stochastic volatility models using asymmetric Laplace error via uniform scale mixtures," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(5), pages 584-608, September.
    3. Jianchang Lin & Debajyoti Sinha & Stuart Lipsitz & Adriano Polpo, 2012. "Semiparametric Bayesian Survival Analysis using Models with Log-linear Median," Biometrics, The International Biometric Society, vol. 68(4), pages 1136-1145, December.
    4. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    5. Juárez, Miguel A. & Steel, Mark F. J., 2010. "Model-Based Clustering of Non-Gaussian Panel Data Based on Skew-t Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 52-66.
    6. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    7. 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.
    8. Debajyoti Sinha & Ming-Hui Chen & Sujit K. Ghosh, 1999. "Bayesian Analysis and Model Selection for Interval-Censored Survival Data," Biometrics, The International Biometric Society, vol. 55(2), pages 585-590, June.
    9. Francisco J. Rubio & Yili Hong, 2016. "Survival and lifetime data analysis with a flexible class of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1794-1813, August.
    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. Saverio Ranciati & Giuliano Galimberti & Gabriele Soffritti, 2019. "Bayesian variable selection in linear regression models with non-normal errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 323-358, June.
    2. Fabrizio Leisen & Luca Rossini & Cristiano Villa, 2020. "Loss-based approach to two-piece location-scale distributions with applications to dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 309-333, 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. Fabrizi, Enrico & Salvati, Nicola & Trivisano, Carlo, 2020. "Robust Bayesian small area estimation based on quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    2. Yingying Hu & Huixia Judy Wang & Xuming He & Jianhua Guo, 2021. "Bayesian joint-quantile regression," Computational Statistics, Springer, vol. 36(3), pages 2033-2053, September.
    3. Francisco J. Rubio & Yili Hong, 2016. "Survival and lifetime data analysis with a flexible class of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1794-1813, August.
    4. 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.
    5. 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.
    6. Yanke Wu & Maozai Tian, 2017. "An effective method to reduce the computational complexity of composite quantile regression," Computational Statistics, Springer, vol. 32(4), pages 1375-1393, December.
    7. 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.
    8. 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.
    9. 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.
    10. Luke B. Smith, 2016. "Discussion," International Statistical Review, International Statistical Institute, vol. 84(3), pages 359-362, December.
    11. Worku B. Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2023. "Flexible two-piece distributions for right censored survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 34-65, January.
    12. 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.
    13. Shiyi Tu & Min Wang & Xiaoqian Sun, 2017. "Bayesian variable selection and estimation in maximum entropy quantile regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(2), pages 253-269, January.
    14. Akosah, Nana Kwame & Alagidede, Imhotep Paul & Schaling, Eric, 2020. "Testing for asymmetry in monetary policy rule for small-open developing economies: Multiscale Bayesian quantile evidence from Ghana," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    15. Paul Hewson & Keming Yu, 2008. "Quantile regression for binary performance indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 401-418, September.
    16. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
    17. Panayi, Efstathios & Peters, Gareth W. & Danielsson, Jon & Zigrand, Jean-Pierre, 2018. "Designating market maker behaviour in limit order book markets," Econometrics and Statistics, Elsevier, vol. 5(C), pages 20-44.
    18. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    19. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    20. James Mitchell & Aubrey Poon & Dan Zhu, 2022. "Constructing Density Forecasts from Quantile Regressions: Multimodality in Macro-Financial Dynamics," Working Papers 22-12R, Federal Reserve Bank of Cleveland, revised 11 Apr 2023.

    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:taf:japsta:v:44:y:2017:i:5:p:798-810. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.