Abstract
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.
Citation
Qiqing Yu. Mo-suk Chow. "Minimaxity of the Empirical Distribution Function in Invariant Estimation." Ann. Statist. 19 (2) 935 - 951, June, 1991. https://doi.org/10.1214/aos/1176348129
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