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Parametric estimation of spatial–temporal point processes using the Stoyan–Grabarnik statistic

Author

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  • Conor Kresin

    (UCLA Department of Statistics)

  • Frederic Schoenberg

    (UCLA Department of Statistics)

Abstract

A novel estimator for the parameters governing spatial–temporal point processes is proposed. Unlike the maximum likelihood estimator, the proposed estimator is fast and easy to compute, and does not require the computation or approximation of a computationally expensive integral. This parametric estimator is based on the Stoyan–Grabarnik (sum of inverse intensity) statistic and is shown to be consistent, under quite general conditions. Simulations are presented demonstrating the performance of the estimator.

Suggested Citation

  • Conor Kresin & Frederic Schoenberg, 2023. "Parametric estimation of spatial–temporal point processes using the Stoyan–Grabarnik statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(6), pages 887-909, December.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:6:d:10.1007_s10463-023-00866-6
    DOI: 10.1007/s10463-023-00866-6
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    References listed on IDEAS

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    1. Mark Berman & T. Rolf Turner, 1992. "Approximating Point Process Likelihoods with Glim," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 31-38, March.
    2. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    3. O Cronie & M N M Van Lieshout, 2018. "A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions," Biometrika, Biometrika Trust, vol. 105(2), pages 455-462.
    4. A. Baddeley & R. Turner & J. Møller & M. Hazelton, 2005. "Residual analysis for spatial point processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 617-666, November.
    5. Yosihiko Ogata & Koichi Katsura, 1988. "Likelihood analysis of spatial inhomogeneity for marked point patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 29-39, March.
    6. Peter J. Diggle & Irene Kaimi & Rosa Abellana, 2010. "Partial-Likelihood Analysis of Spatio-Temporal Point-Process Data," Biometrics, The International Biometric Society, vol. 66(2), pages 347-354, June.
    7. Harte, David, 2010. "PtProcess: An R Package for Modelling Marked Point Processes Indexed by Time," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i08).
    8. 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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    Cited by:

    1. A. C. Micheas, 2025. "Random mixture Cox point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(2), pages 289-330, April.

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