论文标题
具有相变的空间功能数据的变量图
Variograms for spatial functional data with phase variation
论文作者
论文摘要
空间功能数据中的空间，振幅和相变。量化空间变化的流行功能痕量变量图的结论在分析具有相位变化的未对准功能数据时可能会产生误导。为了解决这个问题，我们描述了一个框架，该框架将功能数据中的幅度相分离方法扩展到空间设置，以进行群集和空间预测。我们提出将痕量变化图分解为振幅和相分量，并量化功能观测之间的空间相关性如何在其各自的振幅和相位成分中表现出来。这使我们能够为空间功能数据生成单独的振幅和相聚类方法，并基于组合单独的幅度和相预测，在未观察到的位置开发了一种新型的空间功能插值。通过模拟和实际数据分析，我们发现所提出的方法会产生更准确的预测和更可解释的聚类结果。
Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace variogram, which quantifies spatial variation, can be misleading when analysing misaligned functional data with phase variation. To remedy this, we describe a framework that extends amplitude-phase separation methods in functional data to the spatial setting, with a view towards performing clustering and spatial prediction. We propose a decomposition of the trace variogram into amplitude and phase components and quantify how spatial correlations between functional observations manifest in their respective amplitude and phase components. This enables us to generate separate amplitude and phase clustering methods for spatial functional data, and develop a novel spatial functional interpolant at unobserved locations based on combining separate amplitude and phase predictions. Through simulations and real data analyses, we found that the proposed methods result in more accurate predictions and more interpretable clustering results.
