Abstract: For the problem of estimating a multivariate normal mean, it is known that confidence sets recentered at shrinkage estimators offer strictly larger coverage probability than the usual confidence set. Unfortunately, the conventional frequentist report of a constant confidence coefficient (infimum of the coverage probabilities) fails to communicate the gain of these improved confidence sets. Through an empirical Bayes argument we introduce a confidence report for the recentered confidence set which is strictly larger than the conventional infimum report. This confidence report is shown to dominate the infimum report according to an appropriate risk criterion. By using this new confidence report, the improved confidence region provides an informative frequentist measure of precision for the shrinkage estimator about which it has been recentered.
Key words and phrases: Conditional confidence, loss estimation, shrinkage estimation, Stein estimator.