Structural grouping of extreme value models via graph fused lasso

Abstract: The generalized Pareto distribution (GPD) is a fundamental model for analyzing the tail behavior of a distribution. In particular, the shape parameter of the GPD characterizes the extremal properties of the distribution. As described in this paper, we propose a method for grouping shape parameters in the GPD for clustered data via graph fused lasso. The proposed method simultaneously estimates the model parameters and identifies which clusters can be grouped together. We establish the asymptotic theory of the proposed estimator and demonstrate that its variance is lower than that of the cluster-wise estimator. This variance reduction not only enhances estimation stability but also provides a principled basis for identifying homogeneity and heterogeneity among clusters in terms of their tail behavior. We assess the performance of the proposed estimator through Monte Carlo simulations. As an illustrative example, our method is applied to rainfall data from 996 clustered sites across Japan.