A Counterexample Concerning the Extension of Uniform Strong Laws to Ergodic Processes
نویسندگان
چکیده
We present a construction showing that a class of sets 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.
منابع مشابه
A Counterexample Concerning Uniform Ergodic Theorems for a Class of Functions
Vapnik and Cervonenkis, and Talagrand, have characterized the Glivenko-Cantelli property for independent random variables. We show that these characterizations fail to hold for general stationary ergodic processes. Appears in Statistics and Probability Letters, 24 165-168, 1995. ∗Andrew Nobel is a Beckman Institute Fellow at the University of Illinois Urbana-Champaign. Correspondence to: Andrew...
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