Unified univariate extreme risk modeling through sub-sampling block maxima

Abstract In this paper, we introduce a sub-sampling block maxima approach for constructing and characterizing univariate extreme risk measures.We investigate relationships between block size and block maxima statistics originating from both Gaussian and {gpd}s. We characterize the scaling inherent in extreme risks through the analysis of the {mpmr} and the {evi}. We introduce the {wlse} for {evi}, employ the second moment for plateau finding in {evi} and {ei} estimation, and present the effect of {ei} on the {kld}.The applicability of this approach is demonstrated across a variety of real-world datasets, including meteorite landing mass, earthquake energy release, solar activity, and variations in Greenland's land snow cover and sea ice extent.Our method offers a practical and unified univariate extreme risk measure, capable of capturing a spectrum of extreme risks and accounting for temporal dependence. The approach stands out for its flexibility, sample efficiency, and limited reliance on subjective hyper-parameter tuning, making it a valuable tool in extreme risk modeling. MSC Classification: 62P12