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.

我们介绍由希尔伯特值随机对数强度驱动的一类新的空间Cox过程。我们在光谱域中采用参数框架，以估计其空间功能相关性结构。具体来说，我们考虑一种基于周期图算子的频谱函数方法，其灵感来自Whittle估算方法。在线性情况下，证明了参数估计器的强一致性。我们在对数强度模型的高斯一阶空间自回归希尔伯特情景下的仿真研究中说明了此属性。我们的方法被用于西班牙伊比利亚半岛1980-2015年间呼吸道疾病死亡率的空间功能预测。