IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v23y2011i1p149-163.html
   My bibliography  Save this article

Confidence intervals for nonparametric regression

Author

Listed:
  • Lawrence Brown
  • Xin Fu
  • Linda Zhao

Abstract

In nonparametric function estimation, providing a confidence interval with the right coverage is a challenging problem. This is especially the case when the underlying function has a wide range of unknown degrees of smoothness. Here, we propose two methods of constructing an average coverage confidence interval built from block shrinkage estimation methods. One is based on the James–Stein shrinkage estimator; the other begins with a Bayesian perspective and is based on a modification of the harmonic prior estimator. Simulation shows that these confidence intervals have average coverage close to or above the nominal coverage even when the underlying function is rough and/or the signal-to-noise ratio is small. Both of the confidence intervals perform consistently well across all the investigated test functions even though these functions have very different shapes and smoothness.

Suggested Citation

  • Lawrence Brown & Xin Fu & Linda Zhao, 2011. "Confidence intervals for nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 149-163.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:149-163
    DOI: 10.1080/10485251003753201
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485251003753201
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485251003753201?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. Stuart Barber & Guy P. Nason & Bernard W. Silverman, 2002. "Posterior probability intervals for wavelet thresholding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 189-205, May.
    2. Wenxin Mao & Linda H. Zhao, 2003. "Free‐knot polynomial splines with confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 901-919, November.
    3. Hardle, W. & Marron, J., 1989. "Bootstrap Simultaneous Error Bars For Nonparametric Regression," LIDAM Discussion Papers CORE 1989023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    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. Severance-Lossin, E. & Sperlich, S., 1995. "Estimation of Derivatives for Additive Separable Models," SFB 373 Discussion Papers 1995,60, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. De Munck, Thomas & Chevalier, Philippe & Tancrez, Jean-Sébastien, 2023. "Managing priorities on on-demand service platforms with waiting time differentiation," International Journal of Production Economics, Elsevier, vol. 266(C).
    3. Avishai Mandelbaum & Petar Momčilović, 2017. "Personalized queues: the customer view, via a fluid model of serving least-patient first," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 23-53, October.
    4. Barrow, Devon & Kourentzes, Nikolaos, 2018. "The impact of special days in call arrivals forecasting: A neural network approach to modelling special days," European Journal of Operational Research, Elsevier, vol. 264(3), pages 967-977.
    5. Rouba Ibrahim & Pierre L'Ecuyer, 2013. "Forecasting Call Center Arrivals: Fixed-Effects, Mixed-Effects, and Bivariate Models," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 72-85, May.
    6. Nabil Channouf & Pierre L’Ecuyer & Armann Ingolfsson & Athanassios Avramidis, 2007. "The application of forecasting techniques to modeling emergency medical system calls in Calgary, Alberta," Health Care Management Science, Springer, vol. 10(1), pages 25-45, February.
    7. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    8. Ward Whitt, 2007. "What you should know about queueing models to set staffing requirements in service systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 476-484, August.
    9. Rouba Ibrahim & Mor Armony & Achal Bassamboo, 2017. "Does the Past Predict the Future? The Case of Delay Announcements in Service Systems," Management Science, INFORMS, vol. 63(6), pages 1762-1780, June.
    10. Peter Hall & Joel L. Horowitz, 2012. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP14/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Rouba Ibrahim & Ward Whitt, 2011. "Wait-Time Predictors for Customer Service Systems with Time-Varying Demand and Capacity," Operations Research, INFORMS, vol. 59(5), pages 1106-1118, October.
    12. Alex Roubos & Ger Koole & Raik Stolletz, 2012. "Service-Level Variability of Inbound Call Centers," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 402-413, July.
    13. Qiuping Yu & Gad Allon & Achal Bassamboo & Seyed Iravani, 2018. "Managing Customer Expectations and Priorities in Service Systems," Management Science, INFORMS, vol. 64(8), pages 3942-3970, August.
    14. Bolandifar, Ehsan & DeHoratius, Nicole & Olsen, Tava, 2023. "Modeling abandonment behavior among patients," European Journal of Operational Research, Elsevier, vol. 306(1), pages 243-254.
    15. Josh Reed & Yair Shaki, 2015. "A Fair Policy for the G / GI / N Queue with Multiple Server Pools," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 558-595, March.
    16. Barrow, Devon K., 2016. "Forecasting intraday call arrivals using the seasonal moving average method," Journal of Business Research, Elsevier, vol. 69(12), pages 6088-6096.
    17. Kinshuk Jerath & Anuj Kumar & Serguei Netessine, 2015. "An Information Stock Model of Customer Behavior in Multichannel Customer Support Services," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 368-383, July.
    18. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.
    19. Achal Bassamboo & Assaf Zeevi, 2009. "On a Data-Driven Method for Staffing Large Call Centers," Operations Research, INFORMS, vol. 57(3), pages 714-726, June.
    20. Politis, Dimitris N, 2010. "Model-free Model-fitting and Predictive Distributions," University of California at San Diego, Economics Working Paper Series qt67j6s174, Department of Economics, UC San Diego.

    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:gnstxx:v:23:y:2011:i:1:p:149-163. 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/GNST20 .

    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.