Abstract
In the usual frequentist formulation of testing and interval estimation there is a strong relationship between α-level tests and 1 - α confidence intervals. Such strong relationships do not always persist for post-data, or Bayesian, measures of accuracy of these procedures. We explore the relationship between post-data measures of accuracy of both tests and interval estimates, measures that are derived under a decision-theoretic structure. We find that, in general, there are strong post-data relationships in the one-sided case, and some relationships in the two-sided case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Berger, J. O. and Delampady, M. (1987). Testing precise hypotheses, Statist. Sci., 2, 317–352.
Berger, J. O. and Sellke, T. (1987). Testing a point null hypothesis: the irreconciliability of p-values and evidence (with discussion), J. Amer. Statist. Assoc., 82, 112–122.
Brown, L. D., Johnstone, I. M., and MacGibbon, K. B. (1981). Variation diminishing transformations: a direct approach to total positivity and its statistical applications, J. Amer. Statist. Assoc., 76, 824–832.
Casella, G. and Berger, R. L. (1987). Reconciling evidence in the one-sided testing problem (with discussion), J. Amer. Statist. Assoc., 82, 106–111.
George, E. I. and Casella, G. (1994). An empirical Bayes confidence report, Statistica Sinica, 4, 617–638.
Coutis, C. and Casella, C. (1992). Increasing the confidence in Student's t interval, Ann. Statist., 20, 1501–1513.
Hwang, J. T. and Pemantle, R. (1990). Evaluation of estimators of statistical significance under a class of proper loss functions, Statist. Decisions (to appear).
Hwang, J. T., Casella, G., Robert, C., Wells, M. T., and Farrell, R. H. (1992). Estimation of accuracy in testing, Ann. Statist., 20, 490–509.
Johnstone, I. M. (1988). On inadmissibility of some unbiased estimates of loss, Statistical Decision Theory and Related Topics IV (eds. J. O. Berger and S. S. Gupta), 361–379, Springer, New York.
Karlin, S. (1968). Total Positivity, Stanford University Press, Stanford, CA.
Lu, K. L. and Berger, J. O. (1989a). Estimation of normal means: Frequentist estimation of loss, Ann. Statist., 17, 890–906.
Lu, K. L. and Berger, J. O. (1989b). Estimated confidence procedures for multivariate normal means, J. Statist. Plann. Inference, 23, 1–19.
Robert, C. R. and Caselia, G. (1993). Improved confidence statements for the usual multivariate normal confidence set, Statistical Decision Theory and Related Topics V (eds. J. O. Berger and S. S. Gupta), 351–368, Springer, New York.
Rukhin, A. L. (1988a). Estimated loss and admissible loss estimators, Statistical Decision Theory and Related Topics IV (eds. J. O. Berger and S. S. Gupta), 409–418, Springer, New York.
Rukhin, A. L. (1988b). Loss functions for loss estimation, Ann. Statist., 16, 1262–1269.
Author information
Authors and Affiliations
About this article
Cite this article
Goutis, C., Casella, G. Relationships Between Post-Data Accuracy Measures. Annals of the Institute of Statistical Mathematics 49, 711–726 (1997). https://doi.org/10.1023/A:1003270426974
Issue Date:
DOI: https://doi.org/10.1023/A:1003270426974