A review of regularised estimation methods and cross-validation in spatiotemporal statistics
arxiv(2024)
摘要
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
≥ 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.
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