Abstract
We present a construction showing that a class of sets $\mathcal{C}$ that is Glivenko-Cantelli for an i.i.d. process need not be Glivenko-Cantelli for every stationary ergodic process with the same one dimensional marginal distribution. This result provides a counterpoint to recent work extending uniform strong laws to ergodic processes, and a recent characterization of universal Glivenko Cantelli classes.
Information
Published: 1 January 2013
First available in Project Euclid: 8 March 2013
zbMATH: 1321.60053
MathSciNet: MR3186744
Digital Object Identifier: 10.1214/12-IMSCOLL901
Subjects:
Primary:
60F15
Secondary:
60G10
Keywords:
cutting and stacking
,
ergodic process
,
Glivenko-Cantelli
,
uniform laws of large numbers
Rights: Copyright © 2010, Institute of Mathematical Statistics
