Improved confidence estimators for confidence sets of location parameters

Consider a p-dimensional location family symmetrical about θ. Let Ct(X) be a 1−α confidence set {θ:|t(X)−θ|⩽c} of θ, where t(X) is some reasonable estimator of θ. Traditionally, the confidence coefficient 1−α, which is data independent, is used to be the report for the confidence of Ct(X). In this paper, some improved confidence reports are provided for p⩾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⩽4 are also present in this paper.