On weak approximation of U-statistics

Details On weak approximation of U-statistics On weak approximation of U-statistics

2009-01-15

arxiv.org/abs/0901.2343v1

Mathematics

Probability

12 pages

Scientific paper

This paper investigates weak convergence of U-statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U-statistic exists is relaxed to having 4/3 moments only (modulo a logarithmic term). Furthermore, the conditional expectation of the kernel is only assumed to be in the domain of attraction of the normal law (instead of the classical two-moment condition).

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