Poisson approximation for some statistics based on exchangeable trials
- 1 September 1983
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 15 (3) , 585-600
- https://doi.org/10.2307/1426620
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.Keywords
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