The Annals of Probability

Necessary and sufficient conditions for the strong law of large numbers for U-statistics

Rafał Latała and Joel Zinn

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Abstract

Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the strong law of large numbers for (symmetrized) U-statistics.We also obtain necessary and sufficient conditions for the a.s. convergence of series of an analogous form.

Article information

Source
Ann. Probab., Volume 28, Number 4 (2000), 1908-1924.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160513

Digital Object Identifier
doi:10.1214/aop/1019160513

Mathematical Reviews number (MathSciNet)
MR1813848

Zentralblatt MATH identifier
1044.60025

Subjects
Primary: 60F15: Strong theorems 60E15: Inequalities; stochastic orderings

Keywords
U-statistics strong law of large numbers random series

Citation

Latała, Rafał; Zinn, Joel. Necessary and sufficient conditions for the strong law of large numbers for U -statistics. Ann. Probab. 28 (2000), no. 4, 1908--1924. doi:10.1214/aop/1019160513. https://projecteuclid.org/euclid.aop/1019160513


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References

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