Conditionally acceptable recentered set estimators. (English) Zbl 0629.62013

Casella, George

Ann. Stat. 15, 1363-1371 (1987).

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.

MSC:

62C99	Statistical decision theory
62H12	Estimation in multivariate analysis
62F25	Parametric tolerance and confidence regions

Keywords:

confidence sphere; multivariate normal mean; coverage probability; Stein- type estimator; betting procedures; conditional acceptability; recentered confidence sets; James-Stein estimator