Stein's method and locally dependent point process approximation
msra(2011)
摘要
Random events in space and time often exhibit a locally dependent structure.
When the events are very rare and dependent structure is not too complicated,
various studies in the literature have shown that Poisson and compound Poisson
processes can provide adequate approximations. However, the accuracy of
approximations does not improve or may even deteriorate when the mean number of
events increases. In this paper, we investigate an alternative family of
approximating point processes and establish Stein's method for their
approximations. We prove two theorems to accommodate respectively the
positively and negatively related dependent structures. Three examples are
given to illustrate that our approach can circumvent the technical difficulties
encountered in compound Poisson process approximation [see Barbour &
M{\aa}nsson (2002)] and our approximation error bound decreases when the mean
number of the random events increases, in contrast to increasing bounds for
compound Poisson process approximation.
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关键词
point process,approximation error,compound poisson process,stein s method
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