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Importance of interpolation when constructing double‐bootstrap confidence intervals

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  • Peter Hall
  • Stephen M.‐S. Lee
  • G. Alastair Young

Abstract

We show that, in the context of double‐bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double‐bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error.

Suggested Citation

  • Peter Hall & Stephen M.‐S. Lee & G. Alastair Young, 2000. "Importance of interpolation when constructing double‐bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 479-491.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:2:p:479-491
    DOI: 10.1111/1467-9868.00245
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    Cited by:

    1. Luis Alexander Crouch & Cheng Zheng & Ying Qing Chen, 2017. "Estimating a Treatment Effect in Residual Time Quantiles Under the Additive Hazards Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 298-315, June.
    2. Mst. Papia Sultana and Jialiang Li & Jianhua Hu, 2015. "Comparison of three-dimensional ROC surfaces for clustered and correlated markers, with a proteomics application," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 399-418, November.
    3. Lixia Diao & David D. Smith & Gauri Sankar Datta & Tapabrata Maiti & Jean D. Opsomer, 2014. "Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 497-515, June.

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