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Donsker classes of sets
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  • Published: June 1988

Donsker classes of sets

  • Michel Talagrand1,2 

Probability Theory and Related Fields volume 78, pages 169–191 (1988)Cite this article

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  • 12 Citations

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Summary

We study the central limit theorem (CLT) and the law of large numbers (LLN) for empirical processes indexed by a (countable) class of sets C. The main result, of purely measure-theoretical nature, relates different ways to measure the “size” of C. It relies on a new rearrangement inequality that has been inspired by techniques used in the local theory of Banach spaces. As an application, we give sharp necessary conditions for the CLT, that are in some sense the best possible. We also obtain a way to compute the rate of convergence in the LLN.

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Author information

Authors and Affiliations

  1. Equipe d'Analyse, Université de Paris VI, Place Jussieu, F-75252, Paris Cedex 05, France

    Michel Talagrand

  2. Department of Mathematics, Ohio State University, 43210, Columbus, OH, USA

    Michel Talagrand

Authors
  1. Michel Talagrand
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Talagrand, M. Donsker classes of sets. Probab. Th. Rel. Fields 78, 169–191 (1988). https://doi.org/10.1007/BF00322017

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  • Received: 20 February 1986

  • Issue Date: June 1988

  • DOI: https://doi.org/10.1007/BF00322017

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Keywords

  • Banach Space
  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Statistical Theory
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