Environmental extreme risk modeling via sub-sampling block maxima

Abstract: This paper introduces a novel sub-sampling block maxima technique to model and characterize environmental extreme risks. We examine the relationships between block size and block maxima statistics derived from the Gaussian and generalized Pareto distributions. We introduce a weighted least square estimator for extreme value index (EVI) and evaluate its performance using simulated auto-correlated data. We employ the second moment of block maxima for plateau finding in EVI and extremal index (EI) estimation, and present the effect of EI on Kullback-Leibler divergence. The applicability of this approach is demonstrated across diverse environmental datasets, including meteorite landing mass, earthquake energy release, solar activity, and variations in Greenland's land snow cover and sea ice extent. Our method provides a sample-efficient framework, robust to temporal dependencies, that delivers actionable environmental extreme risk measures across different timescales. With its flexibility, sample efficiency, and limited reliance on subjective tuning, this approach emerges as a useful tool for environmental extreme risk assessment and management.