Bounds for non-Gaussian approximations of U-statistics

Author

Yuri V. Borovskikh and Neville C. Weber

Status

Research Report 2000-17
Date: 16 August 2000

Abstract

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

Content

The paper is available in the following forms:

TeX dvi format:: 2000-17.dvi.gz (46kB) or 2000-17.dvi (152kB)
PostScript:: 2000-17.ps.gz (208kB) or 2000-17.ps (502kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics