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Rates of Poisson convergence for U-statistics

Published online by Cambridge University Press:  14 July 2016

T. C. Brown  and
B. W. Silverman
T. C. Brown
Affiliation:
University of Cambridge
B. W. Silverman
Affiliation:
University of Oxford
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Abstract

Poisson limit theorems for U-statistics are studied. A general rate of convergence is obtained; this rate is improved for the special case where the U-statistic arises from the consideration of distances between uniformly distributed points in a well-behaved plane region.

Keywords

U-STATISTICSPOISSON LIMITTOTAL VARIATION DISTANCESPATIAL PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 428 - 432
Copyright
Copyright © Applied Probability Trust 1979 

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References

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