We address the problem of spatial prediction for Hilbert data, when their spatial domain of observation is a river network. The reticular nature of the domain requires to use geostatistical methods based on the concept of Stream Distance, which captures the spatial connectivity of the points in the river induced by the network branching. Within the framework of Object Oriented Spatial Statistics (O2S2), where the data are considered as points of an appropriate (functional) embedding space, we develop a class of functional moving average models based on the Stream Distance. Both the geometry of the data and that of the spatial domain are thus taken into account. A consistent definition of covariance structure is developed, and associated estimators are studied. Through the analysis of the summer water temperature profiles in the Middle Fork River (Idaho, USA), our methodology proved to be effective, both in terms of covariance structure characterization and forecasting performance.

当希尔伯特数据的观察空间域是河流网络时，我们解决了希尔伯特数据的空间预测问题。该域的网状性质要求使用基于河流距离概念的地统计方法，该方法捕获由网络分支引起的河流中点的空间连通性。在面向对象空间统计（O2S2）的框架内，数据被视为适当（功能）嵌入空间的点，我们开发了一类基于流距离的功能移动平均模型。因此，数据的几何形状和空间域的几何形状都被考虑在内。制定了协方差结构的一致定义，并研究了相关的估计量。通过对中福克河（美国爱达荷州）夏季水温剖面的分析，我们的方法在协方差结构表征和预测性能方面都被证明是有效的。