Improved confidence estimators for confidence sets of location parameters

Consider a p-dimensional location family symmetrical about theta. Let C-t(x) be a 1-alpha confidence set {theta: \t(X) - theta\ less than or equal to c} of theta, where t(X) is some reasonable estimator of theta. Traditionally, the confidence coefficient 1-alpha, which is data independent, is used to be the report for the confidence of C-t(X). In this paper, some improved confidence reports are provided for p greater than or equal to 5. These results are related to Robinson (Ann. Statistic 7 (1979) 756). The normal case discussed in Robinson (Ann. Statistic 7 (1979) 756) is a special case of the results of this paper. Moreover, some admissibility results when p less than or equal to 4 are also present in this paper. (C) 2003 Elsevier B.V. All rights reserved.