This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models. These methods are particularly relevant in the case of big geospatial data for dimensionality reduction or model selection. To structure the review, we initially consider the most general case of multivariate spatiotemporal processes (i.e., $g > 1$ dimensions of the spatial domain, a one-dimensional temporal domain, and $q \geq 1$ random variables). Then, the idea of regularised/penalised estimation procedures and different choices of shrinkage targets are discussed. Finally, guided by the elements of a mixed-effects model, which allows for a variety of spatiotemporal models, we show different regularisation procedures and how they can be used for the analysis of geo-referenced data, e.g. for selection of relevant regressors, dimensionality reduction of the covariance matrices, detection of conditionally independent locations, or the estimation of a full spatial interaction matrix.

翻译：本综述聚焦于适用于地质统计模型与空间计量经济模型的正则化估计方法。这些方法在大规模地理空间数据的降维或模型选择中尤为重要。为结构化综述内容，我们首先考虑多变量时空过程的最一般情形（即空间域维度$g > 1$、一维时间域及随机变量数量$q \geq 1$），继而探讨正则化/惩罚估计方法的基本思想及不同收缩目标的选择。最后，基于混合效应模型框架（该框架支持多种时空模型），我们展示了不同的正则化方法及其在地理参考数据分析中的应用，包括相关回归变量的筛选、协方差矩阵的降维、条件独立位置的检测以及全空间交互矩阵的估计。