The LIL for canonical $U$-statistics

Details The LIL for canonical $U$-statistics The LIL for canonical $U$-statistics

2006-04-11

arxiv.org/abs/math/0604262v2

Annals of Probability 2008, Vol. 36, No. 3, 1023-1058

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP351 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP351

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.

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