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Rates of Convergence and Law of the Iterated Logarithm for U-Processes

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  • Kaoukeb Turki-Moalla

Abstract

We study in this paper some limit theorems for U-processes. We calculate rates of convergence in the central limit theorem of nondegenerate U-processes under metric entropy with bracketing condition. In application, we improve upon the law of the iterated logarithm of Arcones. All calculations use the Ossiander chaining procedure.

Suggested Citation

  • Kaoukeb Turki-Moalla, 1998. "Rates of Convergence and Law of the Iterated Logarithm for U-Processes," Journal of Theoretical Probability, Springer, vol. 11(4), pages 869-906, October.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:4:d:10.1023_a:1022656529912
    DOI: 10.1023/A:1022656529912
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    References listed on IDEAS

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    1. Arcones, M. A., 1993. "The Law of the Iterated Logarithm for U-Processes," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 139-151, October.
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