%0 Generic %1 richards2021spatial %A Richards, Jordan %A Wadsworth, Jennifer L. %D 2021 %K extremalDependence ppt spatial temperature %R 10.1002/env.2671 %T Spatial deformation for non-stationary extremal dependence %U http://arxiv.org/abs/2101.07167 %X Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for modelling non-stationarity in extremal dependence rely on models that are either computationally difficult to fit or require prior knowledge of covariates. Sampson and Guttorp (1992) proposed a simple technique for handling non-stationarity in spatial dependence by smoothly mapping the sampling locations of the process from the original geographical space to a latent space where stationarity can be reasonably assumed. We present an extension of this method to a spatial extremes framework by considering least squares minimisation of pairwise theoretical and empirical extremal dependence measures. Along with some practical advice on applying these deformations, we provide a detailed simulation study in which we propose three spatial processes with varying degrees of non-stationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared to a naive modelling approach.

@misc{richards2021spatial, abstract = {Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for modelling non-stationarity in extremal dependence rely on models that are either computationally difficult to fit or require prior knowledge of covariates. Sampson and Guttorp (1992) proposed a simple technique for handling non-stationarity in spatial dependence by smoothly mapping the sampling locations of the process from the original geographical space to a latent space where stationarity can be reasonably assumed. We present an extension of this method to a spatial extremes framework by considering least squares minimisation of pairwise theoretical and empirical extremal dependence measures. Along with some practical advice on applying these deformations, we provide a detailed simulation study in which we propose three spatial processes with varying degrees of non-stationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared to a naive modelling approach.}, added-at = {2021-06-21T11:50:27.000+0200}, author = {Richards, Jordan and Wadsworth, Jennifer L.}, biburl = {https://www.bibsonomy.org/bibtex/27b54dc66ee45b4ed0c73af7d7a3b1961/simon.brown}, description = {[2101.07167] Spatial deformation for non-stationary extremal dependence}, doi = {10.1002/env.2671}, interhash = {0b8275376cbdb7c7000f4dd602df5bd2}, intrahash = {7b54dc66ee45b4ed0c73af7d7a3b1961}, keywords = {extremalDependence ppt spatial temperature}, note = {cite arxiv:2101.07167Comment: 41 pages, 10 figures}, timestamp = {2021-06-21T11:50:27.000+0200}, title = {Spatial deformation for non-stationary extremal dependence}, url = {http://arxiv.org/abs/2101.07167}, year = 2021 }