Spatial Cox processes in an infinite-dimensional framework. (English) Zbl 1497.60054
Spatial point processes have a lot of applications in many different fields and were studied in various settings. One of them is the particular case of a Cox process which is obtained as an extension of a Poisson process, being a natural model for point process phenomena that are environmentally driven. In this paper, spatial Cox processes in an infinite-dimensional framework are studied. Cox processes driven by a spatial Hilbert-valued log-intensity random field are introduced. Under stationarity in the space, a parametric framework is adopted in the spatial functional spectral domain. Strong consistency of the formulated parametric estimator of the second-order product density is proved. A simulation study is undertaken under a spatial autoregressive Hilbertian process framework to illustrate the obtained results. The approach is applied to the parametric estimation of the eigenvalues and eigenvectors of the involved autocorrelation operators. The obtained model is applied to the spatial functional prediction of respiratory disease mortality in the Spanish Iberian Peninsula, in the time interval 1980–2015. The paper ends with some conclusions and discussions about the obtained results and possibilities to continue this work.
Reviewer: Ilie Valuşescu (Bucureşti)
MSC:
| 60G25 | Prediction theory (aspects of stochastic processes) |
| 60G60 | Random fields |
| 62J05 | Linear regression; mixed models |
| 62J10 | Analysis of variance and covariance (ANOVA) |
Keywords:
infinite-dimensional log-intensity; periodogram operator; respiratory disease mortality; spatial autoregressive Hilbertian processes; spatial Cox processesReferences:
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