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arXiv · 1811.11139

Spatial Cox processes in an infinite-dimensional framework

M. P. Frías·A. Torres-Signes·M. D. Ruiz-Medina·J. Mateu
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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, 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.

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M. P. Frías, A. Torres-Signes, M. D. Ruiz-Medina, J. Mateu. 2021-03-10. Spatial Cox processes in an infinite-dimensional framework. https://arxiv.org/abs/1811.11139

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