arXiv:math/0604262 Abstract

arXiv:math/0604262 [math.PR]Abstract References Reviews Resources

The LIL for canonical $U$-statistics

Published 2006-04-11, updated 2008-06-13Version 2

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.

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

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

DOI: 10.1214/07-AOP351

Categories: math.PR

Subjects: 60E15

Keywords: sufficient conditions, arbitrary order, growth conditions, statistics kernel

Tags: journal article

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