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 oper...

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Bibliographic Details
Published in:Test (Madrid, Spain) Spain), 2022-03, Vol.31 (1), p.175-203
Main Authors: Frías, María P., Torres-Signes, Antoni, Ruiz-Medina, María D., Mateu, Jorge
Format: Article
Language:English
Subjects:
Economics
Finance
Insurance
Management
Mathematics and Statistics
Original Paper
Respiratory diseases
Statistical Theory and Methods
Statistics
Statistics for Business
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Summary: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.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-021-00773-z