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Published online by Cambridge University Press: 01 July 2016
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.