Problem
Research questions and friction points this paper is trying to address.
Extreme Value Theory
non-stationary
data-sparse
tail estimation
risk assessment
The data-driven extreme value distribution: non-parametric tail estimation with a derived stability criterion
🤖 AI Summary
This study addresses the limitations of classical extreme value theory, which relies on asymptotic assumptions and struggles to accurately characterize extreme risks under data sparsity or non-stationarity. The authors propose DDEVD, a nonparametric approach that reconstructs the underlying distribution via kernel density estimation and incorporates superstatistical aggregation, thereby avoiding parametric assumptions about the tail. They derive theoretical conditions for optimal bandwidth selection and stability, establishing the explicit criterion $m < C n^{1+\gamma/2}$ that links extrapolation reliability directly to the extreme value index for the first time. Applied to sub-hourly Alpine precipitation data, DDEVD reliably reproduces 100-year return events using only ten years of observations (calibration ratio: 0.96). In metal micrograph analysis, it improves estimation accuracy for safety-critical grain-size extremes by 58% over the log-normal model.
📝 Abstract
Quantifying the likelihood of extreme events underpins risk assessment, yet classical Extreme Value Theory relies on asymptotic assumptions that fail in the data-sparse, non-stationary regimes practitioners increasingly face. We introduce the Data-Driven Extreme Value Distribution (DDEVD), a non-parametric estimator that aggregates all observations metastatistically and reconstructs the base distribution with a kernel, removing parametric tail assumptions. We derive its optimal bandwidth and prove a stability law $m < C\,n^{1+γ/2}$ relating reliable extrapolation to the extreme value index $γ$. In sub-hourly Alpine precipitation, DDEVD recovers stable 100-year return levels from single decades (calibration ratio $0.96$), departing from the full-record reference by over $50\,\%$ in fewer than one window in fifty -- versus one in five for a GEV fit. In metallurgical micrographs, it matches a generalised extreme-value fit on the safety-relevant grain-size tail, where the standard log-normal over-predicts by $58\,\%$ at $1\,\mathrm{cm}^{2}$.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Data-Driven Extreme Value Distribution
non-parametric tail estimation
extreme value index
stability criterion
kernel reconstruction
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