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Computational issues of generalized fiducial inference

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  • Hannig, Jan
  • Lai, Randy C.S.
  • Lee, Thomas C.M.

Abstract

Generalized fiducial inference is closely related to the Dempster–Shafer theory of belief functions. It is a general methodology for constructing a distribution on a (possibly vector-valued) model parameter without the use of any prior distribution. The resulting distribution is called the generalized fiducial distribution, which can be applied to form estimates and confidence intervals for the model parameter. Previous studies have shown that such estimates and confidence intervals possess excellent frequentist properties. Therefore it is useful and advantageous to be able to calculate the generalized fiducial distribution, or at least to be able to simulate a random sample of the model parameter from it. For a small class of problems this generalized fiducial distribution can be analytically derived, while for some other problems its exact form is unknown or hard to obtain. A new computational method for conducting generalized fiducial inference without knowing the exact closed form of the generalized fiducial distribution is proposed. It is shown that this computational method enjoys desirable theoretical and empirical properties. Consequently, with this proposed method the applicability of generalized fiducial inference is enhanced.

Suggested Citation

  • Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:849-858
    DOI: 10.1016/j.csda.2013.03.003
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    References listed on IDEAS

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    1. Lidong, E. & Hannig, Jan & Iyer, Hari, 2008. "Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 854-865, June.
    2. Jan Hannig & Thomas C. M. Lee, 2009. "Generalized fiducial inference for wavelet regression," Biometrika, Biometrika Trust, vol. 96(4), pages 847-860.
    3. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    4. Wandler, Damian V. & Hannig, Jan, 2011. "Fiducial inference on the largest mean of a multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 87-104, January.
    5. Nagatsuka, Hideki & Kamakura, Toshinari & Balakrishnan, N., 2013. "A consistent method of estimation for the three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 210-226.
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    Cited by:

    1. Seungyong Hwang & Randy C. S. Lai & Thomas C. M. Lee, 2022. "Generalized Fiducial Inference for Threshold Estimation in Dose–Response and Regression Settings," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 109-124, March.

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