The Annals of Probability

The LIL for canonical U-statistics

Radosław Adamczak and 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.

Article information

Source
Ann. Probab. Volume 36, Number 3 (2008), 1023-1058.

Dates
First available in Project Euclid: 9 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1207749089

Digital Object Identifier
doi:10.1214/07-AOP351

Mathematical Reviews number (MathSciNet)
MR2408582

Zentralblatt MATH identifier
1144.60015

Subjects
Primary: 60E15: Inequalities; stochastic orderings

Keywords
U-statistics law of the iterated logarithm

Citation

Adamczak, Radosław; Latała, Rafał. The LIL for canonical U -statistics. Ann. Probab. 36 (2008), no. 3, 1023--1058. doi:10.1214/07-AOP351. https://projecteuclid.org/euclid.aop/1207749089.


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References

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