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Poisson Approximation for Some Statistics Based on Exchangeable Trials

A. D. Barbour and G. K. Eagleson
Advances in Applied Probability
Vol. 15, No. 3 (Sep., 1983), pp. 585-600
DOI: 10.2307/1426620
Stable URL: http://www.jstor.org/stable/1426620
Page Count: 16
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Poisson Approximation for Some Statistics Based on Exchangeable Trials
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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 {Yj}j=1 M be exchangeable random elements of a space H and, for I a k-subset of H, let XI be a 0-1 function. The statistics studied here are of the form W=∑I∈ NXI, where N is some collection of k-subsets of H. 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.

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