The LIL for $U$-statistics in Hilbert spaces

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.

References in corpus (4)

• Estimates of moments and tails of Gaussian chaoses
• Moment inequalities for functions of independent random variables
• Moment inequalities for U-statistics
• The LIL for canonical $U$-statistics