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On Estimation of the Intensity Function of a Point Process

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  • Marie-Colette N. M. Lieshout

    (CWI and Eindhoven University of Technology)

Abstract

In this paper we review techniques for estimating the intensity function of a spatial point process. We present a unified framework of mass preserving general weight function estimators that encompasses both kernel and tessellation based estimators. We give explicit expressions for the first two moments of these estimators in terms of their product densities, and pay special attention to Poisson processes.

Suggested Citation

  • Marie-Colette N. M. Lieshout, 2012. "On Estimation of the Intensity Function of a Point Process," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 567-578, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9244-9
    DOI: 10.1007/s11009-011-9244-9
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    References listed on IDEAS

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    1. Lionel Cucala, 2008. "Intensity Estimation for Spatial Point Processes Observed with Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 322-334, June.
    2. V. Granville, 1998. "Estimation of the intensity of a Poisson point process by means of nearest neighbor distances," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 112-124, March.
    3. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
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    Citations

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    Cited by:

    1. M. N. M. Lieshout, 2020. "Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 995-1008, September.
    2. Camerlenghi, F. & Capasso, V. & Villa, E., 2014. "On the estimation of the mean density of random closed sets," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 65-88.
    3. O. Cronie & M. N. M. Van Lieshout, 2015. "A J -function for Inhomogeneous Spatio-temporal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 562-579, June.
    4. Cholaquidis, Alejandro & Forzani, Liliana & Llop, Pamela & Moreno, Leonardo, 2017. "On the classification problem for Poisson point processes," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 1-15.

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