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Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes

Author

Listed:
  • Michaela Prokešová

    (Charles University)

  • Jiří Dvořák

    (Charles University)

Abstract

In the paper we introduce a flexible inhomogeneous space-time shot-noise Cox process model and derive a two-step estimation procedure for it. In the first step the inhomogeneity is estimated by means of a Poisson score estimating equation and in the second step we use minimum contrast estimation based on second order properties to obtain estimates of the clustering parameters. The suggested model is not separable but it has a special interaction structure which enables to use the spatial and temporal projections of the process for parameter estimation. Efficiency of the introduced method is investigated by means of a simulation study and it is compared to a previously used method.

Suggested Citation

  • Michaela Prokešová & Jiří Dvořák, 2014. "Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 433-449, June.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9324-0
    DOI: 10.1007/s11009-013-9324-0
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    References listed on IDEAS

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    1. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    2. Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.
    3. Anders Brix & Peter J. Diggle, 2001. "Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 823-841.
    4. Edith Gabriel & Peter J. Diggle, 2009. "Second‐order analysis of inhomogeneous spatio‐temporal point process data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 43-51, February.
    5. Jesper Møller & Mohammad Ghorbani, 2012. "Aspects of second-order analysis of structured inhomogeneous spatio-temporal point processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 472-491, November.
    6. Anders Brix & Jesper Moller, 2001. "Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 471-488, September.
    7. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
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