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Abstract:
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Max-stable models have been widely used for describing the dependence structure in multivariate and spatial extremes. They are natural models to use since they are characterized by the max-stability property, which arises in limiting joint distributions for block maxima with block size tending to infinity. However, likelihood-based inference for high-dimensional max-stable distributions is computationally prohibitive. Although the likelihood function has a known general expression, it involves a combinatorial explosion of terms, which makes it impossible to evaluate exactly even in relatively small dimensions. Several strategies have already been proposed to make inference for max-stable models in high dimensions, including composite likelihood inference. In this work, we investigate the performance of the Vecchia approximation for max-stable distributions, which can be viewed as a weighted composite likelihood with carefully selected weights. The Vecchia approximation benefits from the appealing efficiency gains, while dramatically reducing the computational burden. We illustrate the methodology by application to a high-dimensional dataset of Red Sea surface temperature extremes.
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