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).

Key phrases

U-statistics. U-statistical sums. Symmetric degenerate kernel. Gaussian random variables. tail moments.

AMS Subject Classification (1991)

Primary: 60F05
Secondary: 62E20


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