Approaches for Empirical Bayes Confidence Intervals
Abstract
Parametric empirical Bayes methods of point estimation date to the landmark paper of James and Stein (1961). Interval estimation through parametric empirical Bayes techniques has a somewhat shorter history, which is summarized in the recent paper of Laird and Louis (1987). In the exchangeable case, one obtains a naive EB confidence interval by simply taking appropriate percentiles of the estimated posterior distribution of the parameter, where the estimation of the prior parameters (hyperparameters) is accomplished through marginal distribution of the data. Unfortunately, these naive intervals tend to be too short, since they fail to account for the variability in the estimation of the hyperparameters. That is, they don't attain the desired coverage probability in the EB sense defined in Morris (1983a,b). They also provide no statement of conditional calibration (Rubin, 1984). This paper proposes a conditional bias correction method for developing EB intervals which corrects these deficiencies in the naive intervals. As an alternative, several authors have suggested use of the marginal posterior in this regard. We attempt to clarify its role in achieving EB coverage. Results of extensive simulation of coverage probability and interval length for these approaches are presented in the context of several illustrative examples. Keywords: Bias correction, Parametric bootstrap, Conditional calibration.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 02, 1989
- Accession Number
- ADA205775
Entities
People
- Alan E. Gelfand
- Bradley P. Carlin
Organizations
- Stanford University