Probability Theory and Related Fields

, Volume 77, Issue 2, pp 271–305

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

  • Niels T. Andersen
  • Evarist Giné
  • Mina Ossiander
  • Joel Zinn
Article

DOI: 10.1007/BF00334041

Cite this article as:
Andersen, N.T., Giné, E., Ossiander, M. et al. Probab. Th. Rel. Fields (1988) 77: 271. doi:10.1007/BF00334041

Summary

A CLT and a LIL are proved under weak-L2 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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Niels T. Andersen
    • 1
  • Evarist Giné
    • 2
  • Mina Ossiander
    • 3
  • Joel Zinn
    • 2
  1. 1.Department of MathematicsUniversity of AarhusAarhus, CDenmark
  2. 2.Department of MathematicsTexas A & M UniversityCollege StationUSA
  3. 3.Department of MathematicsUniversity of WashingtonSeattleUSA

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