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A note on uniform laws of averages for dependent processes

Author

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  • Nobel, Andrew
  • Dembo, Amir

Abstract

If for a 'permissible' family of functions and an i.i.d. process {Xi}[infinity]i=0, with probability one, then the same holds for away absolutely regular (weakly Bernoulli) process having the same marginal distribution. In particular, for any class of sets having finite V-C dimension and any absolutely regular process {Xi}[infinity]i=0, with probability one.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:3:p:169-172
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    Citations

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    Cited by:

    1. Peligrad, Magda, 2002. "Some remarks on coupling of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 201-209, November.
    2. Taisuke Otsu & Myung Hwan Seo, 2014. "Asymptotics for maximum score method under general conditions," STICERD - Econometrics Paper Series 571, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Karandikar, Rajeeva L. & Vidyasagar, M., 2002. "Rates of uniform convergence of empirical means with mixing processes," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 297-307, July.
    4. Myung Hwan Seo & Taisuke Otsu, 2016. "Local M-estimation with discontinuous criterion for dependent and limited observations," STICERD - Econometrics Paper Series /589, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Salim Bouzebda & Youssouf Souddi & Fethi Madani, 2024. "Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    6. Ghosh Debashis, 2012. "Incorporating the Empirical Null Hypothesis into the Benjamini-Hochberg Procedure," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-21, July.
    7. repec:cep:stiecm:/2014/571 is not listed on IDEAS
    8. Magda Peligrad, 2001. "A Note on the Uniform Laws for Dependent Processes Via Coupling," Journal of Theoretical Probability, Springer, vol. 14(4), pages 979-988, October.
    9. 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.
    10. Antonio Galvao & Kengo Kato & Gabriel Montes-Rojas & Jose Olmo, 2014. "Testing linearity against threshold effects: uniform inference in quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 413-439, April.

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