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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

Steven P. Ellis
Steven P. Ellis*
Affiliation:
Massachusetts Institute of Technology
*
∗Present address: Department of Statistics, University of Rochester, Rochester, NY 14627, USA.
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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.

Keywords

SPATIAL POINT PROCESSSTOCHASTIC INTEGRALFACTORIAL CUMULANT MEASURESDENSITY ESTIMATIONPALM DISTRIBUTIONGAUSS-POISSON PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 3 , September 1987 , pp. 546 - 559
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

This work was partially supported by United States National Science Foundation Grants MCS 75–10376, PFR 79–01642, and MCS 82–02122.

References

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