Statistical analysis of spatio-temporal data has been evolving to handle increasingly large data sets. For example, the North American CORDEX program is producing daily values of climate-related variables on spatial grids with approximately 100,000 locations over 150 years. Smoothing of such massive and noisy data is essential to understanding their spatio-temporal features. It also reduces the size of the data by representing them in terms of suitable basis functions, which facilitates further computations and statistical analysis. Traditional tensor-based methods break down under the size of such massive data. We develop a penalized spline method for representing such data using a generalization of the sandwich smoother proposed by Xiao et al. (2013). Unlike the original method, our generalization treats the spatial and temporal dimensions distinctly and allows the methodology to be directly applied to non-gridded data. We demonstrate the practicality of the methodology using both simulated and real data. The new smoother, as well as the original sandwich smoother, is implemented in the hero R package.

时空数据的统计分析一直在发展，以处理越来越大的数据集。例如，北美CORDEX计划正在150年中在大约100,000个位置的空间网格上生成与气候相关的变量的每日值。如此庞大而嘈杂的数据的平滑处理对于理解其时空特征至关重要。通过以合适的基函数表示数据，它也减小了数据的大小，这有利于进一步的计算和统计分析。传统的基于张量的方法在如此海量数据的大小下分解。我们开发了一种惩罚性样条曲线方法，用于使用Xiao等人提出的三明治平滑器的一般化来表示此类数据。（2013）。与原始方法不同 我们的归纳法清楚地对待了空间和时间维度，并允许该方法直接应用于非网格数据。我们使用模拟和真实数据演示了该方法的实用性。新的平滑器和原始的三明治平滑器在英雄R包。