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Some asymptotic results for fiducial and confidence distributions

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  • Veronese, Piero
  • Melilli, Eugenio

Abstract

Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations are accurate at least to order O(n−1). For the mean parameter μ=(μ1,…,μk) of an exponential family, our fiducial distribution is asymptotically normal and invariant to the importance ordering of the μi’s.

Suggested Citation

  • Veronese, Piero & Melilli, Eugenio, 2018. "Some asymptotic results for fiducial and confidence distributions," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 98-105.
    • Handle: RePEc:eee:stapro:v:134:y:2018:i:c:p:98-105
    DOI: 10.1016/j.spl.2017.10.011
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    References listed on IDEAS

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    1. Bailey K. Fosdick & Adrian E. Raftery, 2012. "Estimating the Correlation in Bivariate Normal Data With Known Variances and Small Sample Sizes," The American Statistician, Taylor & Francis Journals, vol. 66(1), pages 34-41, February.
    2. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
    3. Piero Veronese & Eugenio Melilli, 2015. "Fiducial and Confidence Distributions for Real Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 471-484, June.
    4. Dungang Liu & Regina Y. Liu & Minge Xie, 2015. "Multivariate Meta-Analysis of Heterogeneous Studies Using Only Summary Statistics: Efficiency and Robustness," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 326-340, March.
    5. Jan Hannig & Hari Iyer & Randy C. S. Lai & Thomas C. M. Lee, 2016. "Generalized Fiducial Inference: A Review and New Results," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1346-1361, July.
    6. Jan Hannig & Thomas C. M. Lee, 2009. "Generalized fiducial inference for wavelet regression," Biometrika, Biometrika Trust, vol. 96(4), pages 847-860.
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