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Second-order approximation to the characteristic function of certain point-process integrals
Published online by Cambridge University Press: 01 July 2016
Abstract
A general way to look at kernel estimates of densities is to regard them as stochastic integrals with respect to a spatial point process. Under regularity conditions these behave asymptotically as if the point process were Poisson. However, this Poisson approximation may not work well if the data exhibits a lot of clustering. In this paper a more refined approximation to the characteristic functions of the integrals is developed. For clustered data, a ‘Gauss–Poisson’ approximation works better than the Poisson.
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- Research Article
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- Copyright © Applied Probability Trust 1987
Footnotes
This work was partially supported by United States National Science Foundation Grants MCS 75–10376, PFR 79–01642, and MCS 82–02122.
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