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A counterexample concerning uniform ergodic theorems for a class of functions

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  • Nobel, Andrew

Abstract

Vapnik and Cervonenkis (1971), and Talagrand (1987), have characterized the Glivenko-Cantelli Property for independent random variables. We show that these characterizations fail to hold for stationary ergodic processes.

Suggested Citation

  • Nobel, Andrew, 1995. "A counterexample concerning uniform ergodic theorems for a class of functions," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 165-168, August.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:2:p:165-168
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    References listed on IDEAS

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    1. Nobel, Andrew & Dembo, Amir, 1993. "A note on uniform laws of averages for dependent processes," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 169-172, June.
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    Cited by:

    1. Raffaello Seri & Christine Choirat, 2013. "Scenario Approximation of Robust and Chance-Constrained Programs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 590-614, August.
    2. Hess, Christian & Seri, Raffaello & Choirat, Christine, 2010. "Ergodic theorems for extended real-valued random variables," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1908-1919, September.

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