Rates of Poisson convergence for U-statistics

1 June 1979

journal article
research article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 16 (02), 428-432
https://doi.org/10.1017/s0021900200046635

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-STATISTICS
POISSON LIMIT
TOTAL VARIATION DISTANCE
SPATIAL PROCESSES

This publication has 4 references indexed in Scilit:

A General Poisson Approximation Theorem
The Annals of Probability, 1975
The Poisson Approximation for Dependent Events
The Annals of Probability, 1974
The asymptotic distribution of random clumps
Computing, 1972
A Class of Statistics with Asymptotically Normal Distribution
The Annals of Mathematical Statistics, 1948

Cited by 8 articles