Let $G_n$ be the empirical distribution based on $n$ independent uniform random variables. Criteria for bounds on the supremum of weighted discrepancies between $G_n(u)$ and $u$ of the form: $|w_\nu(u) D_n(u)|$, where $D_n(u) = G_n(u) - u, w_\nu(u) = (u(1 - u))^{-1 + \nu}$ and $0 \leq \nu \leq 1$, are derived. Also an inequality closely related to an equality due to Daniels (1945) is given.
Publié le : 1981-10-14
Classification:
Weighted empirical distributions,
bounds,
uniform order statistics,
60F15,
60617,
62G30
@article{1176994315,
author = {Mason, David M.},
title = {Bounds for Weighted Empirical Distribution Functions},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 881-884},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994315}
}
Mason, David M. Bounds for Weighted Empirical Distribution Functions. Ann. Probab., Tome 9 (1981) no. 6, pp. 881-884. http://gdmltest.u-ga.fr/item/1176994315/