{"title":"A review of regularised estimation methods and cross-validation in spatiotemporal statistics","authors":"Philipp Otto, Alessandro Fassò, Paolo Maranzano","doi":"arxiv-2402.00183","DOIUrl":null,"url":null,"abstract":"This review article focuses on regularised estimation procedures applicable\nto geostatistical and spatial econometric models. These methods are\nparticularly relevant in the case of big geospatial data for dimensionality\nreduction or model selection. To structure the review, we initially consider\nthe most general case of multivariate spatiotemporal processes (i.e., $g > 1$\ndimensions of the spatial domain, a one-dimensional temporal domain, and $q\n\\geq 1$ random variables). Then, the idea of regularised/penalised estimation\nprocedures and different choices of shrinkage targets are discussed. Finally,\nguided by the elements of a mixed-effects model, which allows for a variety of\nspatiotemporal models, we show different regularisation procedures and how they\ncan be used for the analysis of geo-referenced data, e.g. for selection of\nrelevant regressors, dimensionality reduction of the covariance matrices,\ndetection of conditionally independent locations, or the estimation of a full\nspatial interaction matrix.","PeriodicalId":501323,"journal":{"name":"arXiv - STAT - Other Statistics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - STAT - Other Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2402.00183","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.