With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of spatially referenced data collected over time, motivated by environmental studies utilizing remotely sensed satellite data. In particular, we specify a semiparametric autoregressive model without the usual Gaussian assumption and devise a computationally scalable procedure that enables the regression analysis of large datasets. We estimate the model parameters by quasi maximum likelihood and show that the computational complexity can be reduced from cubic to linear of the sample size. Asymptotic properties under suitable regularity conditions are further established that inform the computational procedure to be efficient and scalable. A simulation study is conducted to evaluate the finite-sample properties of the parameter estimation and statistical inference. We illustrate our methodology by a dataset with over 2.96 million observations of annual land surface temperature and the comparison with an existing state-of-the-art approach highlights the advantages of our method.

翻译：随着数据获取技术的迅速发展,时空数据在各种不同的学科中日益丰富。我们在这里开发了时空空间回归法,用于分析长期收集的大量空间参考数据,利用遥感卫星数据进行环境研究的驱动力。特别是,我们指定了半对称自动递减模型,而没有通常的高斯假设,并设计了一个可计算可扩缩的程序,以便能够对大型数据集进行回归分析。我们以准最大的可能性对模型参数进行估计,并表明计算的复杂性可以从样本大小的立方到线。在适当的常规条件下,进一步确定了用于说明计算程序的效率和可缩放的惯性特性。我们进行了模拟研究,以评价参数估计和统计推理的有限抽样特性。我们用一套数据集来说明我们的方法,用296万多年地表温度观测和与现有最新方法的比较来说明我们的方法的优点。