Spatial log-Gaussian Cox processes in Hilbert spaces
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A new class of spatial log-Gaussian Cox processes in function spaces is introduced under suitable conditions. Its least-squares spatial functional predictor is formulated. The special case where the log-intensity is a Gaussian first-order spatial autoregressive Hilbertian process is analysed, and its minimum-contrast componentwise parameter estimation is addressed. The asymptotic properties of these minimum contrast parameter estimators are studied, in a numerical example, in the Web-based Supporting Material. Particularly, the presented approach allows the spatial functional prediction of time, depth or elevation supported curves. An application to respiratory disease mortality curve prediction illustrates the practical relevance of our approach.
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