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.
Publié le : 1991-06-14
Classification:
Minimaxity within a class,
Cramer-von Mises loss,
invariant estimator,
nonparametric estimator,
Egoroff's theorem,
Baire category theorem,
product measure,
62C15,
62D05
@article{1176348129,
author = {Yu, Qiqing and Chow, Mo-suk},
title = {Minimaxity of the Empirical Distribution Function in Invariant Estimation},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 935-951},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348129}
}
Yu, Qiqing; Chow, Mo-suk. Minimaxity of the Empirical Distribution Function in Invariant Estimation. Ann. Statist., Tome 19 (1991) no. 1, pp. 935-951. http://gdmltest.u-ga.fr/item/1176348129/