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The LIL for U-Statistics in Hilbert Spaces

Author

Listed:
  • Radosław Adamczak

    (Polish Academy of Sciences)

  • Rafał Latała

    (Warsaw University)

Abstract

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest.

Suggested Citation

  • Radosław Adamczak & Rafał Latała, 2008. "The LIL for U-Statistics in Hilbert Spaces," Journal of Theoretical Probability, Springer, vol. 21(3), pages 704-744, September.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:3:d:10.1007_s10959-007-0134-6
    DOI: 10.1007/s10959-007-0134-6
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    References listed on IDEAS

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    1. Arcones, Miguel A. & Giné, Evarist, 1995. "On the law of the iterated logarithm for canonical U-statistics and processes," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 217-245, August.
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