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Asymptotic Palm likelihood theory for stationary point processes

  • Michaela Prokešová
  • Eva B. Vedel Jensen
Article

Abstract

In the present paper, we propose a Palm likelihood approach as a general estimating principle for stationary point processes in \(\mathbf{R}^d\) for which the density of the second-order factorial moment measure is available in closed form or in an integral representation. Examples of such point processes include the Neyman–Scott processes and the log Gaussian Cox processes. The computations involved in determining the Palm likelihood estimator are simple. Conditions are provided under which the Palm likelihood estimator is strongly consistent and asymptotically normally distributed.

Keywords

Asymptotic normality Cluster processes Consistency  Neyman–Scott processes Log Gaussian Cox processes Palm likelihood  Spatial point process Strong mixing 

Notes

Acknowledgments

This work was supported by projects GAČR 201/08/P100 and 201/10/0472 from the Czech Science Foundation and by Centre for Stochastic Geometry and Advanced Bioimaging, funded by the Villum Foundation.

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2012

Authors and Affiliations

  1. 1.Department of Probability and Statistics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Department of Mathematics, Centre for Stochastic Geometry and Advanced Bioimaging Aarhus UniversityAarhus CDenmark

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