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October, 1981 Bounds for Weighted Empirical Distribution Functions
David M. Mason
Ann. Probab. 9(5): 881-884 (October, 1981). DOI: 10.1214/aop/1176994315

Abstract

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.

Citation

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David M. Mason. "Bounds for Weighted Empirical Distribution Functions." Ann. Probab. 9 (5) 881 - 884, October, 1981. https://doi.org/10.1214/aop/1176994315

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0478.60036
MathSciNet: MR628880
Digital Object Identifier: 10.1214/aop/1176994315

Subjects:
Primary: 60F15
Secondary: 60617, 62G30

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 5 • October, 1981
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