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Abstract:
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We study the class of dependence models for spatial data obtained from Cauchy convolution processes based on various kernel functions. We show that the proposed models have appealing tail dependence properties, e.g., tail dependence at short distances and independence at long distances. We derive the extreme-value limits of these processes, study their smoothness properties, and detail some interesting special cases. To get higher flexibility at sub-asymptotic levels and separately control the bulk and tail dependencies, we further propose spatial models constructed by mixing a Cauchy convolution process with a Gaussian process. We show that this framework yields a rich class of models for the joint modeling of the bulk and tail behaviors. Our proposed inference approach relies on matching model-based and empirical summaries, and an extensive simulation study shows that it yields accurate estimates. We demonstrate our new methodology by application to a temperature dataset measured at 97 stations in Oklahoma, US. Our results indicate that our proposed model provides a very good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.
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