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The Confidence Density for Correlation

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  • Gunnar Taraldsen

    (Norwegian University of Science and Technology)

Abstract

Inference for correlation is central in statistics. From a Bayesian viewpoint, the final most complete outcome of inference for the correlation is the posterior distribution. An explicit formula for the posterior density for the correlation for the binormal is derived. This posterior is an optimal confidence distribution and corresponds to a standard objective prior. It coincides with the fiducial introduced by R.A. Fisher in 1930 in his first paper on fiducial inference. C.R. Rao derived an explicit elegant formula for this fiducial density, but the new formula using hypergeometric functions is better suited for numerical calculations. Several examples on real data are presented for illustration. A brief review of the connections between confidence distributions and Bayesian and fiducial inference is given in an Appendix.

Suggested Citation

  • Gunnar Taraldsen, 2023. "The Confidence Density for Correlation," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 600-616, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00267-y
    DOI: 10.1007/s13171-021-00267-y
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    References listed on IDEAS

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    1. 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.
    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. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265.
    4. 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.
    5. Gunnar Taraldsen & Bo H. Lindqvist, 2015. "Fiducial and Posterior Sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(17), pages 3754-3767, September.
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