IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v69y2015i1p28-33.html
   My bibliography  Save this article

Monotone B-Spline Smoothing for a Generalized Linear Model Response

Author

Listed:
  • Wei Wang
  • Dylan S. Small

Abstract

Various methods have been proposed for smoothing under the monotonicity constraint. We review the literature and implement an approach of monotone smoothing with B-splines for a generalized linear model response. The approach is expressed as a quadratic programming problem and is easily solved using the statistical software R. In a simulation study, we find that the approach performs better than other approaches with much faster computation time. The approach can also be used for smoothing under other shape constraints or mixed constraints. Supplementary materials of the appendices and R code to implement the developed approach is available online.

Suggested Citation

  • Wei Wang & Dylan S. Small, 2015. "Monotone B-Spline Smoothing for a Generalized Linear Model Response," The American Statistician, Taylor & Francis Journals, vol. 69(1), pages 28-33, February.
  • Handle: RePEc:taf:amstat:v:69:y:2015:i:1:p:28-33
    DOI: 10.1080/00031305.2014.969445
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2014.969445
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/00031305.2014.969445?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. Dette, Holger & Neumeyer, Natalie & Pilz, Kay F., 2005. "A Note on Nonparametric Estimation of the Effective Dose in Quantal Bioassay," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 503-510, June.
    2. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    3. Zheng Wang, 2000. "An algorithm for generalized monotonic smoothing," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(4), pages 495-507.
    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. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    2. Krief, Jerome M., 2017. "Direct instrumental nonparametric estimation of inverse regression functions," Journal of Econometrics, Elsevier, vol. 201(1), pages 95-107.
    3. Zhang, Yu Yvette, 2017. "A shape constrained estimator of bidding function of first-price sealed-bid auctions," Economics Letters, Elsevier, vol. 150(C), pages 67-72.
    4. Wenchuan Liu & Yu Zhang & Qi Li, 2015. "A semiparametric varying coefficient model of monotone auction bidding processes," Empirical Economics, Springer, vol. 48(1), pages 313-335, February.
    5. Charu Sharma & Amber Habib & Sunil Bowry, 2018. "Cluster analysis of stocks using price movements of high frequency data from National Stock Exchange," Papers 1803.09514, arXiv.org.
    6. Birke, Melanie & Dette, Holger, 2006. "Testing strict monotonicity in nonparametric regression," Technical Reports 2006,49, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Shively, Thomas S. & Kockelman, Kara & Damien, Paul, 2010. "A Bayesian semi-parametric model to estimate relationships between crash counts and roadway characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 699-715, June.
    8. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    9. Walter W. Piegorsch & Hui Xiong & Rabi N. Bhattacharya & Lizhen Lin, 2014. "Benchmark Dose Analysis via Nonparametric Regression Modeling," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 135-151, January.
    10. Gattone, Stefano Antonio & Fortuna, Francesca & Evangelista, Adelia & Di Battista, Tonio, 2022. "Simultaneous confidence bands for the functional mean of convex curves," Econometrics and Statistics, Elsevier, vol. 24(C), pages 183-193.
    11. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    12. Daniel R. Jiang & Warren B. Powell, 2015. "An Approximate Dynamic Programming Algorithm for Monotone Value Functions," Operations Research, INFORMS, vol. 63(6), pages 1489-1511, December.
    13. James P. Hughes & Patricia Totten, 2003. "Estimating the Accuracy of Polymerase Chain Reaction–Based Tests Using Endpoint Dilution," Biometrics, The International Biometric Society, vol. 59(3), pages 505-511, September.
    14. Christophe Abraham & Khader Khadraoui, 2015. "Bayesian regression with B-splines under combinations of shape constraints and smoothness properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 150-170, May.
    15. repec:jss:jstsof:18:i04 is not listed on IDEAS
    16. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    17. Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    18. Boudaoud, S. & Rix, H. & Meste, O., 2010. "Core Shape modelling of a set of curves," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 308-325, February.
    19. Jan Humplik & Gašper Tkačik, 2017. "Probabilistic models for neural populations that naturally capture global coupling and criticality," PLOS Computational Biology, Public Library of Science, vol. 13(9), pages 1-26, September.
    20. Bo Hu & Yuan Ji & Kam-Wah Tsui, 2008. "Bayesian Estimation of Inverse Dose Response," Biometrics, The International Biometric Society, vol. 64(4), pages 1223-1230, December.
    21. C Rohrbeck & D A Costain & A Frigessi, 2018. "Bayesian spatial monotonic multiple regression," Biometrika, Biometrika Trust, vol. 105(3), pages 691-707.

    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:amstat:v:69:y:2015:i:1:p:28-33. 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/UTAS20 .

    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.