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.
翻译:我们引入了由Hilbert-估值随机对数强度驱动的新型空间考克斯过程。 我们在光谱域中采用了一个参数框架,以估计其空间功能相关结构。 具体地说,我们根据Whittle估计方法,根据时间图操作员来考虑光谱功能。 线性案例证明了参数估计值的强烈一致性。 我们用高斯第一级空间自动递增Hilbertian情景模拟研究来说明这一特性,用于日志密度模型。 我们的方法适用于1980-2015年期间西班牙伊比利亚半岛呼吸道疾病死亡率的空间功能预测。