Bounds for non-Gaussian approximations of U-statistics
Yuri V. Borovskikh and Neville C. Weber
Research Report 2000-17
Date: 16 August 2000
Degenerate U-statistics of degree two converge in distribution to weighted sums
of mean adjusted, independent, squared, standard normal random variables. Under
minimal moment conditions bounds are established on the error in approximating
the distribution function of the U-statistic by that of the limiting
distribution. These bounds converge to 0 under more general conditions than
those developed by Bentkus and Gotze (1999).
U-statistics. U-statistical sums. Symmetric degenerate kernel. Gaussian
random variables. tail moments.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics