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Annals of Statistics
A class of confidence sets with constant coverage probability for the mean of a p-variate normal distribution is proposed through a pseudo-empirical-Bayes construction. When the dimension is greater than 2, by combining analytical results with some exact numerical calculations the proposed sets are proved to have a uniformly smaller volume than the usual confidence region. Sufficient conditions for the connectedness of the proposed confidence sets are also derived. In addition, our confidencedoi:10.1214/aos/1069362396 fatcat:xjov5sy3j5eh5cj2oeyznce6ge