Author:
Barbour A. D.,Eagleson G. K.
Abstract
Stein's (1970) method of proving limit theorems for sums of dependent random variables is used to derive Poisson approximations for a class of statistics, constructed from finitely exchangeable random variables.Let be exchangeable random elements of a space and, for I a k-subset of , let XI be a 0–1 function. The statistics studied here are of the form
where N is some collection of k -subsets of .An estimate of the total variation distance between the distributions of W and an appropriate Poisson random variable is derived and is used to give conditions sufficient for W to be asymptotically Poisson. Two applications of these results are presented.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference9 articles.
1. Poisson Approximation for Dependent Trials
2. Epidemiology of childhood leukaemia in Northumberland and Durham;Knox;Brit. J. Prev. Soc. Med.,1964
3. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables;Stein;Proc. 6th Berkeley Symp. Math. Statist. Prob.,1970
4. Rates of Poisson convergence for U-statistics
Cited by
67 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献