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Abstract:
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Modeling the extremal dependence structure of spatial data is challenging when it is of a nonstationary nature. In practice, parametric max-stable models are commonly used for modeling spatially-indexed block maxima data, and stationarity is often assumed to make inference easier. However, this assumption is usually unreliable for data observed over a large or complicated domain. In this work, we develop a computationally efficient method for estimating nonstationary dependence structures in max-stable processes, which builds upon and extends an approach recently proposed in the classical Gaussian-based geostatistics framework. Essentially, our approach consists in dividing the spatial domain into a fine grid of subregions, each with its own set of dependence parameters, and then in using the L1 and L2 penalties to impose spatially smooth parameter estimates. We then also subsequently merge the subregions sequentially together with a new algorithm to enhance the model's performance. Here we mainly focus on the popular Brown-Resnick process. Proposed methods are applied to Nepal temperature extreme data, where our method realistically capture nonstationary extremal dependence.
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