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The central limit theorem and the law of iterated logarithm for empirical processes under local conditions
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  • Published: February 1988

The central limit theorem and the law of iterated logarithm for empirical processes under local conditions

  • Niels T. Andersen1,
  • Evarist GinĂ©2,
  • Mina Ossiander3 &
  • …
  • Joel Zinn2 

Probability Theory and Related Fields volume 77, pages 271–305 (1988)Cite this article

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Summary

A CLT and a LIL are proved under weak-L 2 Gaussian bracketing conditions (weaker than the usual ones). These results have wide applicability and in particular provide an improvement of the Jain-Marcus central limit theorem for C(S)-valued random variables.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Aarhus, DK-8000, Aarhus, C, Denmark

    Niels T. Andersen

  2. Department of Mathematics, Texas A & M University, 77843-3368, College Station, TX, USA

    Evarist Giné & Joel Zinn

  3. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    Mina Ossiander

Authors
  1. Niels T. Andersen
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  2. Evarist Giné
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  3. Mina Ossiander
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  4. Joel Zinn
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Additional information

The research of these authors was carried out while visiting Texas A & M University

The research of these authors has been totally or partially supported by the Danish Natural Science Research Council and by the National Science Foundation Grants numbers DMS-83-18610 and DMS-83-01367

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Andersen, N.T., Giné, E., Ossiander, M. et al. The central limit theorem and the law of iterated logarithm for empirical processes under local conditions. Probab. Th. Rel. Fields 77, 271–305 (1988). https://doi.org/10.1007/BF00334041

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  • Received: 14 August 1986

  • Revised: 07 July 1987

  • Issue Date: February 1988

  • DOI: https://doi.org/10.1007/BF00334041

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Keywords

  • Stochastic Process
  • Probability Theory
  • Local Condition
  • Limit Theorem
  • Statistical Theory
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