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General saddlepoint approximations in the bootstrap

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  • Wang, Suojin

Abstract

In Easton and Ronchetti (1986), a method of general saddlepoint approximations is proposed and shown useful, especially in the case of small sample sizes. A possible improvement of the method is suggested to prevent its potential deficiencies and increase its applicability. Easton and Ronchetti's method and its modified version are extended to bootstrap applications. These results provide a satisfactory answer to Davison and Hinkley's (1988) open question on the bootstrap distribution in the AR(1) model.

Suggested Citation

  • Wang, Suojin, 1992. "General saddlepoint approximations in the bootstrap," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 61-66, January.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:1:p:61-66
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    Cited by:

    1. Huang, Xianzhen & Jin, Sujun & He, Xuefeng & He, David, 2019. "Reliability analysis of coherent systems subject to internal failures and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 75-83.
    2. Chaonan Jiang & Davide La Vecchia & Elvezio Ronchetti & Olivier Scaillet, 2023. "Saddlepoint Approximations for Spatial Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1164-1175, April.
    3. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
    4. Kathman, Steven J. & Terrell, George R., 2003. "Poisson approximation by constrained exponential tilting," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 83-89, January.
    5. Huang, Beiqing & Du, Xiaoping, 2008. "Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation," Reliability Engineering and System Safety, Elsevier, vol. 93(2), pages 325-336.
    6. Timothy C. Hesterberg & Barry L. Nelson, 1998. "Control Variates for Probability and Quantile Estimation," Management Science, INFORMS, vol. 44(9), pages 1295-1312, September.
    7. Paul Braden & Timothy Matis & James C. Benneyan & Binchao Chen, 2022. "Estimating X ¯ Statistical Control Limits for Any Arbitrary Probability Distribution Using Re-Expressed Truncated Cumulants," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    8. Boik, Robert J., 2005. "Second-order accurate inference on eigenvalues of covariance and correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 136-171, September.

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