Abstract
AbstractModeling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, nonstationarity will often prevail. Current methods for modeling nonstationarity 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 nonstationarity 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 minimization 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 nonstationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared with a naive modeling approach.
Highlights
Statistical methodology for spatial extremes can increasingly handle data sampled at more observation locations
We presented a simple yet effective approach to modelling non-stationary extremal dependence
Most of our focus is on χ(h∗ij) as the dependence measure, we have shown that this is replaced by other measures, such as χq(h∗ij) and correlation
Summary
Statistical methodology for spatial extremes can increasingly handle data sampled at more observation locations. Non-stationarity in the spatial dependence structure has been studied by Huser and Genton (2016) in the context of max-stable models, through incorporation of a non-stationary variogram This approach requires knowledge of relevant covariates, and asymptotically dependent maxstable models for spatial extremes have been shown to be too inflexible for many spatial datasets (Wadsworth and Tawn, 2012, Davison et al, 2013, Huser et al, 2017, Huser and Wadsworth, 2019). Because this method is not tailored to extremal dependence, it was neccesary to assume that patterns in non-stationarity were similar for both the extremal and non-extremal dependence structures.
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