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Second-order approximation to the characteristic function of certain point-process integrals

  • Steven P. Ellis (a1)


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.


Corresponding author

Present address: Department of Statistics, University of Rochester, Rochester, NY 14627, USA.


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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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