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Abstract:
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An important goal of extremes modeling is to estimate the T-year return level together with its confidence interval (CI). Spatial extremes are common for climate data as the observations are usually referenced by geographic locations and correlated when they are nearby. The return level estimation for spatial extremes rely on the models particular suitable for spatial extremes including max-stable models, copula, Bayesian methods, spatial generalized extreme value (GEV). Among those methods, spatial GEV is the simplest and fastest approach at the price of ignoring the correlation among observations, yet simulations show that return level estimation using spatial GEV still provides satisfactory results compared to other computationally intensive methods. However, the usual assumption for shape parameter to be an unknown constant over the whole spatial domain for large spatial extremes becomes unrealistic and the return level estimation is sensitive to the shape parameter. We propose a fast approach based on spatial GEV that allows the shape parameter to vary smoothly over the spatial domain using fused lasso and fused ridge. Bootstrap methods are applied to estimate the CI.
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