The LIL for canonical $U$-statistics

Radosław Adamczak; Rafał Latała

doi:10.1214/07-AOP351

The LIL for canonical $U$-statistics

Probability 2008-06-17 v2

Authors: Radosław Adamczak , Rafał Latała

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Abstract

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.

Keywords

limit theorems log canonical geometry

Cite

@article{arxiv.math/0604262,
  title  = {The LIL for canonical $U$-statistics},
  author = {Radosław Adamczak and Rafał Latała},
  journal= {arXiv preprint arXiv:math/0604262},
  year   = {2008}
}

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)

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