  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 setup, 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.
