Spatial Cox processes in an infinite-dimensional framework

María P. Frías (), Antoni Torres-Signes (), María D. Ruiz-Medina () and Jorge Mateu ()
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María P. Frías: University of Jaén
Antoni Torres-Signes: University of Málaga
María D. Ruiz-Medina: University of Granada
Jorge Mateu: University Jaume I

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 1, No 8, 175-203

Abstract: 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.

Keywords: Infinite-dimensional log-intensity; Periodogram operator; Respiratory disease mortality; Spatial Autoregressive Hilbertian processes; Spatial Cox processes; 60G25; 60G60; 62J05; 62J10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11749-021-00773-z

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