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Spatial Cox processes in an infinite-dimensional framework

Author

Listed:
  • María P. Frías

    (University of Jaén)

  • Antoni Torres-Signes

    (University of Málaga)

  • María D. Ruiz-Medina

    (University of Granada)

  • Jorge Mateu

    (University Jaume I)

Abstract

We introduce a new class of spatial Cox processes driven by a Hilbert-valued random log-intensity. We adopt a parametric framework in the spectral domain, to estimate its spatial functional correlation structure. Specifically, we consider a spectral functional, approach based on the periodogram operator, inspired on Whittle estimation methodology. Strong consistency of the parametric estimator is proved in the linear case. We illustrate this property in a simulation study under a Gaussian first-order Spatial Autoregressive Hilbertian scenario for the log-intensity model. Our method is applied to the spatial functional prediction of respiratory disease mortality in the Spanish Iberian Peninsula, in the period 1980–2015.

Suggested Citation

  • María P. Frías & Antoni Torres-Signes & María D. Ruiz-Medina & Jorge Mateu, 2022. "Spatial Cox processes in an infinite-dimensional framework," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 175-203, March.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00773-z
    DOI: 10.1007/s11749-021-00773-z
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    References listed on IDEAS

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    8. Rasmus Waagepetersen & Yongtao Guan & Abdollah Jalilian & Jorge Mateu, 2016. "Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 77-96, January.
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