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Rates of convergence for U-Statistics with varying kernels

Published online by Cambridge University Press:  17 April 2009

N.C. Weber
N.C. Weber
Affiliation:
Department of Mathematical Statistics, University of Sydney, Sydney, New South Wales 2006, Australia.
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Abstract

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Let Un be a U-statistic whose kernel depends on the size n of the sample under consideration. It is shown that when Un is suitably normalised its distribution function differs in Lp norm from the distribution function of a standard normal variable by a term of O(n-½).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 1 - 5
Copyright
Copyright © Australian Mathematical Society 1980

References

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