Spatial Cox processes in an infinite-dimensional framework
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.
Cite
@article{arxiv.1811.11139,
title = {Spatial Cox processes in an infinite-dimensional framework},
author = {M. P. Frías and A. Torres-Signes and M. D. Ruiz-Medina and J. Mateu},
journal= {arXiv preprint arXiv:1811.11139},
year = {2021}
}
Comments
Submitted (25 pages, 18 figures and seven tables)