Clustering Extreme Value Indices in Large Panels

We analyze a large panel of units grouped by shared extreme value indices (EVIs) and aim to identify these unknown groups. To achieve this, we order the Hill estimates of individual EVIs and segment them by minimizing the total squared distance between each estimate and its corresponding group average. We show that our method consistently recovers group memberships, and we establish the asymptotic normality of the proposed group estimator. The group estimator attains a faster convergence rate than the individual Hill estimator, leading to improved estimation accuracy. Simulation results reveal that our method achieves high empirical segmentation accuracy, and the resulting group EVI estimates substantially reduce mean absolute errors compared to individual estimates. We apply the proposed method to analyze a rainfall dataset collected from 4,735 stations across Europe, covering the winter seasons from January 1, 1950, to December 31, 2020, and find statistically significant evidence of an increase in the highest and a decrease in the lowest group EVI estimates, suggesting growing variability and intensification of extreme rainfall events across Europe.