The possibility of improving on the usual multivariate normal confidence was first discussed in Stein (1962). Using the ideas of shrinkage, through Bayesian and empirical Bayesian arguments, domination results, both analytic and numerical, have been obtained. Here we trace some of the developments in confidence set estimation.
"Shrinkage Confidence Procedures." Statist. Sci. 27 (1) 51 - 60, February 2012. https://doi.org/10.1214/10-STS319