It is proved that the classical estimation procedures for the mean of a normal distribution with known variance are minimax solutions of properly formulated problems. A result of Stein and Wald  is an immediate consequence. Other such optimum properties follow. Sequential and non-sequential problems can be treated in this manner. Interval and point estimation are discussed.
"Minimax Estimates of the Mean of a Normal Distribution with Known Variance." Ann. Math. Statist. 21 (2) 218 - 230, June, 1950. https://doi.org/10.1214/aoms/1177729840