The LIL for canonical U-statistics

Radosław Adamczak; Rafał Latała

doi:10.1214/07-AOP351

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Home > Journals > Ann. Probab. > Volume 36 > Issue 3 > Article

May 2008 The LIL for canonical U-statistics

Radosław Adamczak, Rafał Latała

Ann. Probab. 36(3): 1023-1058 (May 2008). DOI: 10.1214/07-AOP351

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Abstract

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical U-statistics of arbitrary order d, extending the previously known results for d=2. The nasc’s are expressed as growth conditions on a parameterized family of norms associated with the U-statistics kernel.