Admissibility of the constant-coverage probability estimator for estimating the coverage function of certain confidence interval

Consider a confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The constant coverage probability is the usual estimator for the coverage function of this interval. Wang (1995) have shown that this estimator is inadmissible under the squared error loss, if p [greater-or-equal, slanted] 5. In this paper, we consider the case where p [less-than-or-equals, slant] 4 and prove that it is admissible under the same loss.