Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data points. The goal of this article is to apply an existing subsampling strategy to standard spatial additive models and to derive the spatial statistical properties. We call this strategy the ''spatial data subset model'' (SDSM) approach, which can be applied to big datasets in a computationally feasible way. Our approach has the advantage that one does not require any additional restrictive model assumptions. That is, computational gains increase as model assumptions are removed when using our model framework. This provides one solution to the computational bottlenecks that occur when applying methods such as Kriging to ''big data''. We provide several properties of this new spatial data subset model approach in terms of moments, sill, nugget, and range under several sampling designs. An advantage of our approach is that it subsamples without throwing away data, and can be implemented using datasets of any size that can be stored. We present the results of the spatial data subset model approach on simulated datasets, and on a large dataset consists of 150,000 observations of daytime land surface temperatures measured by the MODIS instrument onboard the Terra satellite.

翻译：在空间统计学中，基于弱平稳过程假设的加性空间统计模型已成为标准方法。然而这类模型的计算时间会随数据点数量急剧增加，成为其显著缺陷。本文旨在将现有子采样策略应用于标准空间加性模型，并推导其空间统计性质。我们将该策略称为"空间数据子集模型"（SDSM）方法，可在大规模数据集上实现计算可行性。本方法的优势在于无需附加限制性模型假设——实际上，采用我们的模型框架时，计算收益会随模型假设的减少而提升。这为克里金法等模型在"大数据"场景中遇到的计算瓶颈提供了解决方案。我们从矩、基台值、块金值和变程等角度，在多种采样设计下论证该新型空间数据子集模型的性质。本方法的另一优势在于子采样过程中不会丢弃原始数据，且可应用于任意可存储规模的数据集。我们通过模拟数据集以及由Terra卫星MODIS设备采集的15万条白天地表温度观测数据组成的实测数据集，展示了空间数据子集模型方法的实际效果。