Generalized fiducial inference via discretization

Statistica Sinica

Volumn 23, Issue 2, 2013, Pages 489-514

  Hannig, Jan ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Asymptotic properties; Bernstein von Mises theorem; Dempster Shafer calculus; Generalized fiducial inference

Indexed keywords

EID: 84879225534     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: 10.5705/ss.2011.102     Document Type: Article

References (34)

1. Barnard, G. A. (1995). Pivotal models and the fiducial argument. Internat. Statist. Rev. 63, 309-323.
2. Berger, J. O., Bernardo, J. M. and Sun, D. (2009). The formal definition of reference priors. Ann. Statist. 37, 905-938.
3. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd edition. Pacific Grove, CA: Wadsworth and Brooks/Cole Advanced Books and Software.
4. Cordero, R., Seckmeyer, G. and Labbe, F. (2006). Effect of resolution on the uncertainty evaluation. Metrologia 43, 33-38.
5. Davison, A. C., Fraser, D. A. S. and Reid, N. (2006). Improved likelihood inference for discrete data. J. R. Stat. Soc. Ser. B Stat. Methodol. 68, 495-508.
6. Dawid, A. P. and Stone, M. (1982). The functional-model basis of fiducial inference. Ann. Statist. 10, 1054-1074.
7. Dempster, A. P. (1963). On direct probabilites. J. Roy. Statist. Soc. Ser. B 25, 100-110.
8. Dempster, A. P. (2008). The Dempster-Shafer Calculus for Statisticians. Internat. J. Approximate Reasoning 48, 365-377.
9. E, L., Hannig, J. and Iyer, H. K. (2008). Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model. J. Amer. Statist. Assoc. 103, 854-865.
10. E, L., Hannig, J. and Iyer, H. K. (2009). Fiducial Generalized Confidence interval for Median Lethal Dose (LD50). preprint.
11. Efron, B. (1986). Why isn't everyone a Bayesian? Amer. Statist. 40, 1-11. With discussion and a reply by the author.
12. Fisher, R. A. (1930). Inverse probability. Proceedings of the Cambridge Philosophical Society xxvi, 528-535.
13. Fraser, A. M., Fraser, D. A. S. and Staicu, A.-M. (2010). The second order ancillary: A differential view with continuity. Bernoulli 16, 1208-1223.
14. Fraser, D. A. S. (1968). The Structure of Inference. New York-London-Sydney, Wiley.
15. Fraser, D. A. S., Reid, N., Marras, E. and Yi, G. Y. (2010). Default priors for Bayesian and frequentist inference. j. Roy. Statist. Soc. Ser. B 72, 631-654.
16. Frenkel, R. B. and Kirkup, L. (2005). Monte Carlo-based estimation of uncertainty owing to limited resolution of digital instruments. Metrologia 42, 27-30.
17. Hannig, J. (2009). On generalized fiducial inference. Statist. Sinica 19, 491-544.
18. Hannig, J., Iyer, H. K. and Patterson, P. (2006). Fiducial generalized confidence intervals. J. Amer. Statist. Assoc. 101, 254-269.
19. Hannig, J., Iyer, H. K. and Wang, J. C.-M. (2007). Fiducial approach to uncertainty assessment: accounting for error due to instrument resolution. Metrologia 44, 476-483.
20. Hannig, J. and Lee, T. C. M. (2009). Generalized fiducial inference for wavelet regression. Biometrika 96, 847-860.
21. Lindley, D. V. (1958). Fiducial distributions and Bayes' theorem. J. Roy. Statist. Soc. Ser. B 20, 102-107.
22. Shafer, G. (2011). A betting interpretation of Dempster-Shafer degrees of belief. Internat. J. Approximate Reasoning 52, 127-136.
23. Stein, C. M. (1985). On the coverage probability of confidence sets based on a prior distribution. In Sequential methods in statistics, Volume 16 of Banach Center Publ., 485-514. Warsaw: Polish Scientific Publishers PWN.
24. Tibshirani, R. (1989). Noninformative priors for one parameter of many. Biometrika 76, 604-608.
25. Tsui, K.-W. and Weerahandi, S. (1989). Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84, 602-607.
26. Wandler, D. V. and Hannig, J. (2011). Fiducial inference on the largest mean of a multivariate normal distribution. J. Multivariate Anal. 102, 87-104.
27. Wandler, D. V. and Hannig, J. (2012a). A fiducial approach to multiple comparisons. J. Statist. Plann. Inference 142, 878-895.
28. Wandler, D. V. and Hannig, J. (2012b). Generalized fiducial confidence intervals for extremes. Extremes 15, 67-87.
29. Weerahandi, S. (1993). Generalized confidence intervals. J. Amer. Statist. Assoc. 88, 899-905.
30. Wilkinson, G. N. (1977). On resolving the controversy in statistical inference. J. Roy. Statist. Soc. Ser. B 39, 119-171.
31. Willink, R. (2007). On the uncertainty of the mean of digitized measurements. Metrologia 44, 73-81.
32. Witkowsky, V. and Wimmer, G. (2009). Interval estimation of the mean of a normal distribution based on quantized observations. Mathematica Slovaca 59, 627-645.
33. Zabell, S. L. (1992). R. A. Fisher and the fiducial argument. Statist. Sci. 7, 369-387.
34. Zhang, J. and Liu, C. (2011). Dempster-Shafer inference with weak beliefs. Statist. Sinica 21, 475-494.