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March, 1977 Uniform Convergence of the Empirical Distribution Function Over Convex Sets
W. F. Eddy, J. A. Hartigan
Ann. Statist. 5(2): 370-374 (March, 1977). DOI: 10.1214/aos/1176343801


The empirical distribution function $P_n$ converges with probability 1 to a true distribution $P$ in $R^k$, uniformly over measurable convex sets, if and only if $P$ is a countable mixture of distributions, each of which is carried by a flat and gives zero probability to the relative boundaries of convex sets included in the flat.


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W. F. Eddy. J. A. Hartigan. "Uniform Convergence of the Empirical Distribution Function Over Convex Sets." Ann. Statist. 5 (2) 370 - 374, March, 1977.


Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0355.60031
MathSciNet: MR431344
Digital Object Identifier: 10.1214/aos/1176343801

Primary: 60F15
Secondary: 52A20

Keywords: convex sets , Empirical distribution , Glivenko-Cantelli theorem , Uniform convergence

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 2 • March, 1977
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