Garthwaite, P. H. and Buckland, S. T.
Generating Monte Carlo confidence intervals by the Robbins-Monro Process.
Journal of the Royal Statistical Society: Series C (Applied Statistics), 41(1)
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.
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