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Distance Estimates for Poisson Process Approximations of Dependent Thinnings
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Dominic Schuhmacher, Universität Zürich, Switzerland
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Abstract
It is well known, that under certain conditions, gradual thinning
of a point process
on R+d, accompanied by a contraction of space to
compensate for the thinning, leads in
the weak limit to a Cox process. In this article, we apply discretization and a result
based on Stein's method to give estimates of the Barbour-Brown distance d2
between the distribution of a thinned point process and an approximating Poisson
process, and evaluate the estimates in concrete examples. We work in terms of two,
somewhat different, thinning models. The main model is based on the
usual thinning notion of deleting points
independently according to probabilities supplied by a random field.
In Section 4, however, we use an
alternative thinning model, which can be more straightforward to
apply if the thinning is determined by point interactions.
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Full text: PDF
Pages: 165-201
Published on: February 28, 2005
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