Simultaneous confidence regions and simultaneous prediction regions are considered using the expected coverage measure criterion of Naiman. Invariance methods are used to construct minimax procedures in multivariate linear models.
"Simultaneous Estimation and Prediction Using the Expected Coverage Measure Criterion." Ann. Statist. 16 (1) 265 - 277, March, 1988. https://doi.org/10.1214/aos/1176350704