Minimaxity of the Empirical Distribution Function in Invariant Estimation
Qiqing Yu, Mosuk Chow · The Annals of Statistics · 1991
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.