The LIL for canonical $U$-statistics

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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.
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)

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Probability, 60E15 (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/163026

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604262
 http://arxiv.org/abs/math/0604262
 Annals of Probability 2008, Vol. 36, No. 3, 1023-1058
 doi:10.1214/07-AOP351

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