A closed form for the harmonic-prior Bayes estimator with associated confidence sets for the mean of a multivariate normal distribution

In this dissertation, explicit closed form expressions are derived for the harmonic prior Bayes estimator of the mean of a multivariate normal distribution. These closed form expressions facilitate the practical application of this minimax competitor to the James-Stein estimator. These expressions also facilitate the construction and assessment of associated confidence sets obtained as Gaussian approximations to exact Highest Posterior Density regions. In particular, we show by a numerical study that such confidence sets are good competitors to the usual confidence spheres in terms of providing smaller size for nearly equal frequentist coverage. We illustrate the practical potential of our methods by applying them to the original Efron-Morris baseball data.