Spatial Cox processes in an infinite-dimensional framework

• María P. Frías ^[1] ; Antoni Torres-Signes ^[2] ; María D. Ruiz-Medina ^[3] ; Jorge Mateu ^[4]
  1. [1] Universidad de Jaén

     Universidad de Jaén

     Jaén, España

     
  2. [2] Universidad de Málaga

     Universidad de Málaga

     Málaga, España

     
  3. [3] Universidad de Granada

     Universidad de Granada

     Granada, España

     
  4. [4] Department of Mathematics, University Jaume I, Castellón, Spain

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 31, Nº. 1, 2022, págs. 175-203
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.