Consider the problem of continuous invariant estimation of a distribution function with the weighted Cramer-von Mises loss. The minimaxity of the empirical distribution function, which is also the best invariant estimator, is proved for any sample size. This solves a long-standing conjecture.
"Minimaxity of the Empirical Distribution Function in Invariant Estimation." Ann. Statist. 19 (2) 935 - 951, June, 1991. https://doi.org/10.1214/aos/1176348129