Conditionally Acceptable Recentered Set Estimators
The Annals of Statistics · 1987 · Volume 15 · Issue 4
Abstract
The usual confidence sphere for a multivariate normal mean can be uniformly improved upon, in terms of coverage probability, by recentering it at a Stein-type estimator. However, these improved sets can have poor conditional performance. Using the theory of relevant betting procedures, which provides an objective means for assessing the conditional performance of a statistical procedure, a criterion for conditional acceptability can be established. A method of constructing such sets is outlined and applied to some recentered confidence sets. In particular, recentering at the positive-part James-Stein estimator yields a conditionally acceptable confidence set.
Keywords
62C99, 62F10, Betting procedures, Confidence sets, multivariate normal
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