Prior-Free Probabilistic Prediction of Future Observations

References

• Beran, R. (1990), Calibrating Prediction Regions, Journal of the American Statistical Association, 85, 715–723.
   Web of Science ®Google Scholar
• Bhaumik, D.K., Gibbons, R.D. (2004), An Upper Prediction Limit for the Arithmetic Mean of a Lognormal Random Variable, Technometrics, 46, 239–248.
   Web of Science ®Google Scholar
• Coelho, C.A., Mexia, J.T. (2007), On the Distribution of the Product and Ratio of Independent Generalized Gamma-Ratio Random Variables, Sankhyā, 69, 221–255.
   Google Scholar
• Dempster, A.P. (2008), The Dempster–Shafer Calculus for Statisticians, International Journal of Approximate Reasoning, 48, 365–377.
   Web of Science ®Google Scholar
• Eaton, M.L. (1989), Group Invariance Applications in Statistics, Hayward, CA: Institute of Mathematical Statistics.
   Google Scholar
• Fertig, K.W., Mann, N.R. (1977), One-Sided Prediction Intervals for at Least p out of m Future Observations from a Normal Population, Technometrics, 19, 167–167.
   Web of Science ®Google Scholar
• Fisher, R.A. (1959), Statistical Methods and Scientific Inference ( 2nd ed. revised), New York: Hafner Publishing Company.
   Google Scholar
• Fraser, D. A.S. (1968), The Structure of Inference, New York: Wiley.
   Google Scholar
• Geisser, S. (1993), Predictive Inference, Monographs on Statistics and Applied Probability (Vol. 55), New York: Chapman and Hall.
   Google Scholar
• Hahn, G.J., and Meeker, W.Q. (1991), Statistical Intervals: A Guide for Practitioners, New York: Wiley.
   Google Scholar
• Hamada, M., Johnson, V., Moore, L.M., Wendelberger, J. (2004), Bayesian Prediction Intervals and Their Relationship to Tolerance Intervals, Technometrics, 46, 452–459.
   Web of Science ®Google Scholar
• Hannig, J. (2009), On Generalized Fiducial Inference, Statistica Sinica, 19, 491–544.
   Web of Science ®Google Scholar
• ——— (2013), Generalized Fiducial Inference Via Discretization, Statistica Sinica, 23, 489–514.
   Web of Science ®Google Scholar
• Kim, H.-J. (2007), A Monte Carlo Method for Estimating Prediction Limit for the Arithmetic Mean of Lognormal Sample, Communications in Statistics — Theory and Methods, 36, 2159–2167.
   Web of Science ®Google Scholar
• Klenke, A., Mattner, L. (2010), Stochastic Ordering of Classical Discrete Distributions, Advances in Applied Probability, 42, 392–410.
   Web of Science ®Google Scholar
• Krishnamoorthy, K., Mathew, T., Mukherjee, S. (2008), Normal-based Methods for a Gamma Distribution: Prediction and Tolerance Intervals and Stress-strength Reliability, Technometrics, 50, 69–78.
   Web of Science ®Google Scholar
• Lawless, J.F., Fredette, M. (2005), Frequentist Prediction Intervals and Predictive Distributions, Biometrika, 92, 529–542.
   Web of Science ®Google Scholar
• Liu, C., Martin, R. ( 2015), Frameworks for Prior-free Posterior Probabilistic Inference, WIREs Computational Statistics, 7, 77--85.
   Google Scholar
• Martin, R. (2014), Random Sets and Exact Confidence Regions, Sankhyā A, 76, 288–304.
   Google Scholar
• Martin, R., Liu, C. (2013), Inferential Models: A Framework for Prior-Free Posterior Probabilistic Inference, Journal of the American Statistical Association, 108, 301–313.
   Web of Science ®Google Scholar
• ——— ( 2015a), Conditional Inferential Models: Combining Information for Prior-free Probabilistic Inference, Journal of the Royal Statistical Society, . Series B, . 77, 195--217.
   Google Scholar
• ——— ( 2015b), Marginal Inferential Models: Prior-Free Probabilistic Inference on Interest Parameters, Journal of the American Statistical Association1101621--1631. doi: 10.1080/01621459.2014.985827
   Web of Science ®Google Scholar
• Molchanov, I. (2005), Theory of Random Sets, Probability and its Applications (New York), London: Springer-Verlag London Ltd.
   Google Scholar
• Odeh, R.E. (1990), Two-Sided Prediction Intervals to Contain at Least k Out of m Future Observations from a Normal Distribution, Technometrics, 32, 203–216.
   Web of Science ®Google Scholar
• Ott, W.R. (1995), Environmental Statistics and Data Analysis, Boca Raton, FL: CRC Press.
   Google Scholar
• Shafer, G. (1976), A Mathematical Theory of Evidence, Princeton, NJ: Princeton University Press.
   Google Scholar
• Tuyl, F., Gerlach, R., Mengersen, K. (2009), Posterior Predictive Arguments in Favor of the Bayes-Laplace Prior as the Consensus Prior for Binomial and Multinomial Parameters, Bayesian Analysis, 4, 151–158.
   Web of Science ®Google Scholar
• Wang, C.M., Hannig, J., Iyer, H.K. (2012), Fiducial Prediction Intervals, Journal of Statistical Planning and Inference, 142, 1980–1990.
   Web of Science ®Google Scholar
• Wang, H. (2010), Closed Form Prediction Intervals Applied for Disease Counts, The American Statistician, 64, 250–256.
   Web of Science ®Google Scholar
• Xie, M., Singh, K. (2013), Confidence Distribution, the Frequentist Distribution of a Parameter—A Review, International Statistical Review, 81, 3–39.
   Web of Science ®Google Scholar