IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v41y1992i1p159-171.html
   My bibliography  Save this article

Generating Monte Carlo Confidence Intervals by the Robbins–Monro Process

Author

Listed:
  • Paul H. Garthwaite
  • Stephen T. Buckland

Abstract

A new use of the Robbins–Monro search process to generate Monte Carlo confidence intervals for a single‐parameter density function is described. When the optimal value of a ‘step length constant’ is known, asymptotically the process gives exact confidence intervals and is fully efficient. We modify the process for the case where the optimal step length constant is unknown and find that it has low bias and typically achieves an efficiency above 75% for 90% and 95% confidence intervals and above 65% for 99% intervals. Multiple‐sample mark–recapture data are used to illustrate the method.

Suggested Citation

  • Paul H. Garthwaite & Stephen T. Buckland, 1992. "Generating Monte Carlo Confidence Intervals by the Robbins–Monro Process," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 159-171, March.
    • Handle: RePEc:bla:jorssc:v:41:y:1992:i:1:p:159-171
    DOI: 10.2307/2347625
    as

    Download full text from publisher

    File URL: https://doi.org/10.2307/2347625
    Download Restriction: no
    File URL: https://libkey.io/10.2307/2347625?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    2. Lee, Stephen M.S. & Young, G. Alastair, 2005. "Parametric bootstrapping with nuisance parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 143-153, February.
    3. G. Alastair Young, 2003. "Better bootstrapping by constrained prepivoting," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 227-242.
    4. Magnar Lillegard & Steinar Engen, 1999. "Exact confidence intervals generated by conditional parametric bootstrapping," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 447-459.
    5. Gatta, Valerio & Marcucci, Edoardo & Scaccia, Luisa, 2015. "On finite sample performance of confidence intervals methods for willingness to pay measures," Transportation Research Part A: Policy and Practice, Elsevier, vol. 82(C), pages 169-192.
    6. Hristos Tyralis & Demetris Koutsoyiannis & Stefanos Kozanis, 2013. "An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters," Computational Statistics, Springer, vol. 28(4), pages 1501-1527, August.
    7. (Yale) Gong, Yeming & Yücesan, Enver, 2012. "Stochastic optimization for transshipment problems with positive replenishment lead times," International Journal of Production Economics, Elsevier, vol. 135(1), pages 61-72.
    8. Menéndez, P. & Fan, Y. & Garthwaite, P.H. & Sisson, S.A., 2014. "Simultaneous adjustment of bias and coverage probabilities for confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 35-44.

    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:bla:jorssc:v:41:y:1992:i:1:p:159-171. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.