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arXiv · 0704.1643

The LIL for $U$-statistics in Hilbert spaces

Radosław Adamczak·Rafał Latała
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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.

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Radosław Adamczak, Rafał Latała. 2007-04-12. The LIL for $U$-statistics in Hilbert spaces. https://doi.org/10.1007/s10959-007-0134-6

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