ar X iv : 0 90 1 . 23 43 v 1 [ m at h . PR ] 1 5 Ja n 20 09 On weak approximation of U - statistics
نویسنده
چکیده
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 43 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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