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Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes

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  • D'Angelo, Nicoletta
  • Adelfio, Giada
  • Mateu, Jorge

Abstract

A local version of spatio-temporal log-Gaussian Cox processes is proposed by using Local Indicators of Spatio-Temporal Association (LISTA) functions plugged into the minimum contrast procedure, to obtain space as well as time-varying parameters. The new procedure resorts to the joint minimum contrast fitting method to estimate the set of second-order parameters. This approach has the advantage of being suitable in both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. Simulation studies to assess the performance of the proposed fitting procedure are presented, and an application to seismic spatio-temporal point pattern data is shown.

Suggested Citation

  • D'Angelo, Nicoletta & Adelfio, Giada & Mateu, Jorge, 2023. "Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002596
    DOI: 10.1016/j.csda.2022.107679
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    References listed on IDEAS

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    1. Marianna Siino & Francisco J. Rodríguez‐Cortés & Jorge Mateu & Giada Adelfio, 2018. "Testing for local structure in spatiotemporal point pattern data," Environmetrics, John Wiley & Sons, Ltd., vol. 29(5-6), August.
    2. Padoan, Simone A. & Bevilacqua, Moreno, 2015. "Analysis of Random Fields Using CompRandFld," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i09).
    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. 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.
    6. 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.
    7. 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.
    8. Zhuang J. & Ogata Y. & Vere-Jones D., 2002. "Stochastic Declustering of Space-Time Earthquake Occurrences," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 369-380, June.
    9. Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.
    10. Nicoletta D’Angelo & Marianna Siino & Antonino D’Alessandro & Giada Adelfio, 2022. "Local spatial log-Gaussian Cox processes for seismic data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 633-671, December.
    11. Guan, Yongtao, 2006. "A Composite Likelihood Approach in Fitting Spatial Point Process Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1502-1512, December.
    12. J. Pfanzagl, 1969. "On the measurability and consistency of minimum contrast estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 14(1), pages 249-272, December.
    13. 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).
    14. Schlather, Martin & Malinowski, Alexander & Menck, Peter J. & Oesting, Marco & Strokorb, Kirstin, 2015. "Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i08).
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