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Bootstrapping survival times in stochastic systems by using saddlepoint approximations

Author

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  • Ronald W. Butler
  • Douglas A. Bronson

Abstract

The single bootstrap is implemented by using a saddlepoint approximation to determine estimates for the survival and hazard functions of first‐passage times in complicated semi‐Markov processes. The double bootstrap is also implemented by resampling saddlepoint inversions and provides BCa confidence bands for these functions. Confidence intervals for the mean and variance of first‐passage times are easily computed. A new characterization of the asymptotic hazard rate for survival times is presented and leads to an indirect method for constructing its bootstrap confidence interval.

Suggested Citation

  • Ronald W. Butler & Douglas A. Bronson, 2002. "Bootstrapping survival times in stochastic systems by using saddlepoint approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 31-49, January.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:1:p:31-49
    DOI: 10.1111/1467-9868.00323
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    Cited by:

    1. D H Collins & A V Huzurbazar, 2008. "System reliability and safety assessment using non-parametric flowgraph models," Journal of Risk and Reliability, , vol. 222(4), pages 667-674, December.
    2. Robert L. Paige & A. Alexandre Trindade & P. Harshini Fernando, 2009. "Saddlepoint‐Based Bootstrap Inference for Quadratic Estimating Equations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 98-111, March.
    3. Ronald W. Butler & Douglas A. Bronson, 2014. "Multistate Survival Models as Transient Electrical Networks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 167-186, March.
    4. Lô, Serigne N. & Heritier, Stephane & Hudson, Malcolm, 2009. "Saddlepoint approximation for semi-Markov processes with application to a cardiovascular randomised study," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 683-698, January.

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