The LIL for $U$-statistics in Hilbert spaces

Details The LIL for $U$-statistics in Hilbert spaces The LIL for $U$-statistics in Hilbert spaces

2007-04-12

arxiv.org/abs/0704.1643v1

Mathematics

Probability

Scientific paper

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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