Spatial Cox processes in an infinite-dimensional framework

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.

Automated summary

In this study, a new class of spatial Cox processes driven by a Hilbert-valued random log-intensity is introduced. A parametric framework in the spectral domain is adopted to estimate the spatial functional correlation structure, with strong consistency of the parametric estimator proved in the linear case. The method is applied to predict respiratory disease mortality in the Spanish Iberian Peninsula from 1980 to 2015.