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Statistical modeling of a nonstationary spatial extremal dependence structureis challenging. Parametric max-stable processes (MSPs) are common choices formodeling spatially-indexed block maxima, where an assumption of stationarity isusual to make inference feasible. However, this assumption is unrealistic fordata observed over a large or complex domain. We develop acomputationally-efficient method for estimating extremal dependence using aglobally nonstationary but locally-stationary MSP construction, with thespatial domain divided into a fine grid of subregions, each with its owndependence parameters. We use LASSO ($L_1$) or ridge ($L_2$) penalties toobtain spatially-smooth parameter estimates. We then develop a noveldata-driven algorithm to merge homogeneous neighboring subregions. Thealgorithm facilitates model parsimony and interpretability. To make our modelsuitable for high-dimensional data, we exploit a pairwise likelihood to performinference and discuss its computational and statistical efficiency. We applyour proposed method to model monthly maximum temperature data at over 1400sites in Nepal and the surrounding Himalayan and sub-Himalayan regions; we showsignificant improvements in model fit compared to a stationary model.Furthermore, we demonstrate that the estimated merged partition isinterpretable from a geographic perspective and leads to better modeldiagnostics by adequately reducing the number of parameters.

Flexible Modeling of Nonstationary Extremal Dependence Using Spatially-Fused LASSO and Ridge Penalties