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Generating Monte Carlo Confidence Intervals by the Robbins–Monro Process

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  • 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
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    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. 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.
    3. 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.
    4. Lee, Stephen M.S. & Young, G. Alastair, 2005. "Parametric bootstrapping with nuisance parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 143-153, February.
    5. 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.
    6. 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.
    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.

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