Estimated confidence under ancillary statistic everywhere-valid constraint

Consider the problem of estimating the coverage function of an usual confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The usual constant coverage probability estimator is shown to be admissible under the ancillary statistic everywhere-valid constraint. Note that this estimator is not admissible under the usual sense if p≥5. Since the criterion of admissibility under the ancillary statistic everywhere-valid constraint is a reasonable one, that the constant coverage probability estimator has been commonly accepted is justified.