Poisson approximation for some statistics based on exchangeable trials
1983 ◽
Vol 15
(03)
◽
pp. 585-600
◽
Keyword(s):
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.
2002 ◽
Vol 34
(03)
◽
pp. 609-625
◽
2002 ◽
Vol 34
(3)
◽
pp. 609-625
◽
1993 ◽
Vol 25
(02)
◽
pp. 334-347
◽
2003 ◽
Vol 40
(02)
◽
pp. 376-390
◽
2001 ◽
Vol 38
(4)
◽
pp. 882-897
◽
2001 ◽
Vol 38
(04)
◽
pp. 882-897
◽