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Exact confidence intervals generated by conditional parametric bootstrapping

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  • Magnar Lillegard
  • Steinar Engen

Abstract

Conditional parametric bootstrapping is defined as the samples obtained by performing the simulations in such a way that the estimator is kept constant and equal to the estimate obtained from the data. Order statistics of the bootstrap replicates of the parameter chosen in each simulation provide exact confidence intervals, in a probabilistic sense, in models with one parameter under quite general conditions. The method is still exact in the case of nuisance parameters when these are location and scale parameters, and the bootstrapping is based on keeping the maximum-likelihood estimates constant. The method is also exact if there exists a sufficient statistic for the nuisance parameters and if the simulations are performed conditioning on this statistic. The technique may also be used to construct prediction intervals. These are generally not exact, but are likely to be good approximations.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:4:p:447-459
    DOI: 10.1080/02664769922331
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    References listed on IDEAS

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    1. 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.
    2. N/A, 1984. "Confidence Intervals," National Institute Economic Review, National Institute of Economic and Social Research, vol. 109(1), pages 33-37, August.
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