Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T06:03:14.461Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Freedman, D. (1974) The Poisson approximation for dependent events. Ann. Prob. 2, 256–269.CrossRefGoogle Scholar
[2] Hafner, R. (1972) The asymptotic distribution of random clumps. Computing 10, 335–351.Google Scholar
[3] Hoeffding, W. (1948) A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19, 293–325.Google Scholar
[4] Santaló, L. (1976) Integral Geometry and Geometric Probability. Addison-Wesley, Reading, Mass.Google Scholar
[5] Serfling, R. J. (1975) A general Poisson approximation theorem. Ann. Prob. 3, 726–731.CrossRefGoogle Scholar
[6] Silverman, B. and Brown, T. (1978) Short distances, flat triangles and Poisson limits. J. Appl. Prob. 15, 816–826.Google Scholar